(\frac{(n+2)!}{n!}) का सरल रूप क्या है?
What is the simplified form of (\frac{(n+2)!}{n!})?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (n+2)
B (n(n+1))
C ((n+2)(n+1))
D (2n)
Explanation opens after your attempt
Correct Answer
C. ((n+2)(n+1))
Step 1
Concept
((n+2)!=(n+2)(n+1)n!), so (n!) cancels. The remaining part is ((n+2)(n+1)).
Step 2
Why this answer is correct
The correct answer is C. ((n+2)(n+1)). ((n+2)!=(n+2)(n+1)n!), so (n!) cancels. The remaining part is ((n+2)(n+1)).
Step 3
Exam Tip
((n+2)!=(n+2)(n+1)n!), इसलिए (n!) कट जाएगा। शेष ((n+2)(n+1)) है।
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यदि (n=3), तो ((n+2)!) का मान क्या है?
If (n=3), what is the value of ((n+2)!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (24)
B (120)
C (720)
D (6)
Explanation opens after your attempt
Step 1
Concept
(n+2=5), so ((n+2)!=5!=120). First find the value inside the brackets.
Step 2
Why this answer is correct
The correct answer is B. (120). (n+2=5), so ((n+2)!=5!=120). First find the value inside the brackets.
Step 3
Exam Tip
(n+2=5), इसलिए ((n+2)!=5!=120)। पहले कोष्ठक का मान निकालें।
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\(\frac{8!}{5!}\) का मान क्या है?
What is the value of \(\frac{8!}{5!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (336)
B (120)
C (56)
D (720)
Explanation opens after your attempt
Step 1
Concept
\(\frac{8!}{5!}=8\times7\times6=336\). Expand down to the smaller factorial and cancel.
Step 2
Why this answer is correct
The correct answer is A. (336). \(\frac{8!}{5!}=8\times7\times6=336\). Expand down to the smaller factorial and cancel.
Step 3
Exam Tip
\(\frac{8!}{5!}=8\times7\times6=336\)। छोटे फैक्टोरियल तक विस्तार करके काटें।
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\(2!\times4!\) का मान क्या है?
What is the value of \(2!\times4!\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (36)
B (42)
C (48)
D (56)
Explanation opens after your attempt
Step 1
Concept
(2!=2) and (4!=24), so the product is (48). First find factorial values and then multiply.
Step 2
Why this answer is correct
The correct answer is C. (48). (2!=2) and (4!=24), so the product is (48). First find factorial values and then multiply.
Step 3
Exam Tip
(2!=2) और (4!=24), इसलिए गुणनफल (48) है। पहले फैक्टोरियल मान निकालकर फिर गुणा करें।
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(6!-5!) का मान क्या होगा?
What will be the value of (6!-5!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (600)
B (500)
C (720)
D (120)
Explanation opens after your attempt
Step 1
Concept
(6!=720) and (5!=120), so the difference is (600). Write the value of the larger factorial carefully.
Step 2
Why this answer is correct
The correct answer is A. (600). (6!=720) and (5!=120), so the difference is (600). Write the value of the larger factorial carefully.
Step 3
Exam Tip
(6!=720) और (5!=120), इसलिए अंतर (600) है। बड़े फैक्टोरियल का मान ध्यान से लिखें।
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(3!+4!) का मान क्या है?
What is the value of (3!+4!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (24)
B (30)
C (36)
D (42)
Explanation opens after your attempt
Step 1
Concept
(3!=6) and (4!=24), so the sum is (30). Find factorial values before adding them.
Step 2
Why this answer is correct
The correct answer is B. (30). (3!=6) and (4!=24), so the sum is (30). Find factorial values before adding them.
Step 3
Exam Tip
(3!=6) और (4!=24), इसलिए योग (30) है। फैक्टोरियल को जोड़ने से पहले उसका मान निकालें।
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\(\frac{7!}{6!,1!}\) का मान क्या है?
What is the value of \(\frac{7!}{6!,1!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (6)
B (7)
C (14)
D (1)
Explanation opens after your attempt
Step 1
Concept
\(\frac{7!}{6!,1!}=\frac{7\times6!}{6!\times1}=7\). The value of (1!) is (1).
Step 2
Why this answer is correct
The correct answer is B. (7). \(\frac{7!}{6!,1!}=\frac{7\times6!}{6!\times1}=7\). The value of (1!) is (1).
Step 3
Exam Tip
\(\frac{7!}{6!,1!}=\frac{7\times6!}{6!\times1}=7\)। (1!) का मान (1) होता है।
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(\frac{(n+1)!}{n!}) का सरल रूप क्या है?
What is the simplified form of (\frac{(n+1)!}{n!})?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (n)
B (n+1)
C (n!)
D (1)
Explanation opens after your attempt
Step 1
Concept
((n+1)!=(n+1)n!), so division leaves (n+1). Remember the factorial identity.
Step 2
Why this answer is correct
The correct answer is B. (n+1). ((n+1)!=(n+1)n!), so division leaves (n+1). Remember the factorial identity.
Step 3
Exam Tip
((n+1)!=(n+1)n!), इसलिए भाग देने पर (n+1) बचता है। फैक्टोरियल पहचान को याद रखें।
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\(\frac{9!}{9!}\) का मान क्या है?
What is the value of \(\frac{9!}{9!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (0)
B (9)
C (1)
D (81)
Explanation opens after your attempt
Step 1
Concept
Any non-zero quantity divided by itself is (1). Therefore, \(\frac{9!}{9!}=1\).
Step 2
Why this answer is correct
The correct answer is C. (1). Any non-zero quantity divided by itself is (1). Therefore, \(\frac{9!}{9!}=1\).
Step 3
Exam Tip
किसी भी अशून्य समान संख्या का अपने आप से भाग (1) होता है। इसलिए \(\frac{9!}{9!}=1\) है।
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\(1\times2\times3\times4\times5\times6\) को किस रूप में लिखेंगे?
How will you write \(1\times2\times3\times4\times5\times6\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (5!)
B (6!)
C (7!)
D \(6^2\)
Explanation opens after your attempt
Step 1
Concept
The product from (1) to (6) is (6!). In factorial multiplication, writing in reverse or forward order gives the same value.
Step 2
Why this answer is correct
The correct answer is B. (6!). The product from (1) to (6) is (6!). In factorial multiplication, writing in reverse or forward order gives the same value.
Step 3
Exam Tip
(1) से (6) तक का गुणनफल (6!) होता है। फैक्टोरियल में क्रम उल्टा या सीधा लिखने से मान नहीं बदलता।
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(4!) का सही विस्तार कौन सा है?
Which is the correct expansion of (4!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (4+3+2+1)
B \(4\times4\times4\times4\)
C \(4\times3\times2\times1\)
D \(4\times3+2\times1\)
Explanation opens after your attempt
Correct Answer
C. \(4\times3\times2\times1\)
Step 1
Concept
(4!) means \(4\times3\times2\times1\). Factorial uses multiplication, not addition.
Step 2
Why this answer is correct
The correct answer is C. \(4\times3\times2\times1\). (4!) means \(4\times3\times2\times1\). Factorial uses multiplication, not addition.
Step 3
Exam Tip
(4!) का अर्थ \(4\times3\times2\times1\) है। फैक्टोरियल में जोड़ नहीं, गुणा होता है।
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\(\frac{10!}{8!}\) का मान क्या है?
What is the value of \(\frac{10!}{8!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (80)
B (90)
C (100)
D (720)
Explanation opens after your attempt
Step 1
Concept
\(\frac{10!}{8!}=10\times9=90\). Cancelling factorials makes the calculation shorter.
Step 2
Why this answer is correct
The correct answer is B. (90). \(\frac{10!}{8!}=10\times9=90\). Cancelling factorials makes the calculation shorter.
Step 3
Exam Tip
\(\frac{10!}{8!}=10\times9=90\)। फैक्टोरियल काटने से गणना छोटी हो जाती है।
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(0!+1!+2!) का मान क्या है?
What is the value of (0!+1!+2!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
(0!=1), (1!=1), and (2!=2), so the sum is (4). Do not forget to take (0!) as (1).
Step 2
Why this answer is correct
The correct answer is B. (4). (0!=1), (1!=1), and (2!=2), so the sum is (4). Do not forget to take (0!) as (1).
Step 3
Exam Tip
(0!=1), (1!=1) और (2!=2), इसलिए योग (4) है। (0!) को (1) लेना न भूलें।
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(5!-4!) का मान क्या है?
What is the value of (5!-4!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (96)
B (72)
C (48)
D (24)
Explanation opens after your attempt
Step 1
Concept
(5!=120) and (4!=24), so the difference is (96). Find both factorials separately before subtracting.
Step 2
Why this answer is correct
The correct answer is A. (96). (5!=120) and (4!=24), so the difference is (96). Find both factorials separately before subtracting.
Step 3
Exam Tip
(5!=120) और (4!=24), इसलिए अंतर (96) है। घटाने से पहले दोनों फैक्टोरियल अलग निकालें।
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\(\frac{6!}{3!,3!}\) का मान क्या है?
What is the value of \(\frac{6!}{3!,3!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (10)
B (15)
C (18)
D (20)
Explanation opens after your attempt
Step 1
Concept
\(\frac{6!}{3!,3!}=\frac{720}{6\times6}=20\). Keep each factorial value carefully.
Step 2
Why this answer is correct
The correct answer is D. (20). \(\frac{6!}{3!,3!}=\frac{720}{6\times6}=20\). Keep each factorial value carefully.
Step 3
Exam Tip
\(\frac{6!}{3!,3!}=\frac{720}{6\times6}=20\)। हर फैक्टोरियल का मान सावधानी से रखें।
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\(\frac{4!}{2!}\) का सरल मान क्या है?
What is the simplified value of \(\frac{4!}{2!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (8)
B (10)
C (12)
D (16)
Explanation opens after your attempt
Step 1
Concept
\(\frac{4!}{2!}=\frac{24}{2}=12\). Cancelling the factorial part also gives the same answer.
Step 2
Why this answer is correct
The correct answer is C. (12). \(\frac{4!}{2!}=\frac{24}{2}=12\). Cancelling the factorial part also gives the same answer.
Step 3
Exam Tip
\(\frac{4!}{2!}=\frac{24}{2}=12\)। फैक्टोरियल भाग को काटकर भी यही उत्तर मिलता है।
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\(3!\times2!\) का मान क्या है?
What is the value of \(3!\times2!\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (12)
B (10)
C (8)
D (6)
Explanation opens after your attempt
Step 1
Concept
(3!=6) and (2!=2), so the product is (12). Convert factorials into ordinary multiplication to solve.
Step 2
Why this answer is correct
The correct answer is A. (12). (3!=6) and (2!=2), so the product is (12). Convert factorials into ordinary multiplication to solve.
Step 3
Exam Tip
(3!=6) और (2!=2), इसलिए गुणनफल (12) है। फैक्टोरियल को सामान्य गुणा में बदलकर हल करें।
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\(\frac{5!}{3!}\) का मान क्या होगा?
What will be the value of \(\frac{5!}{3!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (10)
B (15)
C (20)
D (30)
Explanation opens after your attempt
Step 1
Concept
\(\frac{5!}{3!}=5\times4=20\). Write the larger factorial up to the smaller factorial and cancel.
Step 2
Why this answer is correct
The correct answer is C. (20). \(\frac{5!}{3!}=5\times4=20\). Write the larger factorial up to the smaller factorial and cancel.
Step 3
Exam Tip
\(\frac{5!}{3!}=5\times4=20\)। बड़े फैक्टोरियल को छोटे फैक्टोरियल तक लिखकर काटें।
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यदि (n!=24), तो (n) का मान क्या है?
If (n!=24), what is the value of (n)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(4!=4\times3\times2\times1=24\), so (n=4). Remembering small factorial values is useful.
Step 2
Why this answer is correct
The correct answer is B. (4). \(4!=4\times3\times2\times1=24\), so (n=4). Remembering small factorial values is useful.
Step 3
Exam Tip
\(4!=4\times3\times2\times1=24\), इसलिए (n=4)। छोटे फैक्टोरियल के मान याद रखना उपयोगी है।
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\(9\times8\times7\) को फैक्टोरियल रूप में कैसे लिखा जा सकता है?
How can \(9\times8\times7\) be written in factorial form?
#factorial_notation
#permutations_combinations
#class_11
#easy
A \(\frac{9!}{6!}\)
B \(\frac{9!}{7!}\)
C \(\frac{8!}{6!}\)
D \(\frac{7!}{9!}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{9!}{6!}\)
Step 1
Concept
\(9!=9\times8\times7\times6!\), so \(\frac{9!}{6!}=9\times8\times7\). Divide by the factorial after the last required factor.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{9!}{6!}\). \(9!=9\times8\times7\times6!\), so \(\frac{9!}{6!}=9\times8\times7\). Divide by the factorial after the last required factor.
Step 3
Exam Tip
\(9!=9\times8\times7\times6!\), इसलिए \(\frac{9!}{6!}=9\times8\times7\)। अंतिम शेष संख्या के बाद वाले फैक्टोरियल से भाग दें।
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\(\frac{8!}{7!}\) का मान क्या है?
What is the value of \(\frac{8!}{7!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (7)
B (15)
C (56)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(\frac{8!}{7!}=8\) because \(8!=8\times7!\). Keep the factorial expansion short in such questions.
Step 2
Why this answer is correct
The correct answer is D. (8). \(\frac{8!}{7!}=8\) because \(8!=8\times7!\). Keep the factorial expansion short in such questions.
Step 3
Exam Tip
\(\frac{8!}{7!}=8\) क्योंकि \(8!=8\times7!\)। ऐसे प्रश्नों में फैक्टोरियल विस्तार छोटा रखें।
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(4!+2!) का मान क्या है?
What is the value of (4!+2!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (26)
B (28)
C (24)
D (22)
Explanation opens after your attempt
Step 1
Concept
(4!=24) and (2!=2), so the total is (26). Find each factorial value before adding.
Step 2
Why this answer is correct
The correct answer is A. (26). (4!=24) and (2!=2), so the total is (26). Find each factorial value before adding.
Step 3
Exam Tip
(4!=24) और (2!=2), इसलिए कुल (26) है। जोड़ने से पहले हर फैक्टोरियल का मान निकालें।
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(n!) को किस रूप में लिखा जा सकता है?
Which form can represent (n!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (n+(n-1)!)
B (n(n-1)!)
C (n-(n-1)!)
D (\frac{n}{(n-1)!})
Explanation opens after your attempt
Correct Answer
B. (n(n-1)!)
Step 1
Concept
(n!=n(n-1)!) is the correct identity. This formula is used often in factorial questions.
Step 2
Why this answer is correct
The correct answer is B. (n(n-1)!). (n!=n(n-1)!) is the correct identity. This formula is used often in factorial questions.
Step 3
Exam Tip
(n!=n(n-1)!) सही पहचान है। फैक्टोरियल के सवालों में यह सूत्र बार-बार काम आता है।
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\(\frac{7!}{5!,2!}\) का मान क्या है?
What is the value of \(\frac{7!}{5!,2!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (14)
B (21)
C (35)
D (42)
Explanation opens after your attempt
Step 1
Concept
\(\frac{7!}{5!,2!}=\frac{7\times6}{2}=21\). Break the larger factorial down to the smaller factorial first.
Step 2
Why this answer is correct
The correct answer is B. (21). \(\frac{7!}{5!,2!}=\frac{7\times6}{2}=21\). Break the larger factorial down to the smaller factorial first.
Step 3
Exam Tip
\(\frac{7!}{5!,2!}=\frac{7\times6}{2}=21\)। पहले बड़े फैक्टोरियल को छोटे फैक्टोरियल तक तोड़ें।
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\(\frac{6!}{4!}\) का सरल मान क्या है?
What is the simplified value of \(\frac{6!}{4!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (24)
B (120)
C (30)
D (10)
Explanation opens after your attempt
Step 1
Concept
\(\frac{6!}{4!}=6\times5=30\). Cancelling the common factorial part is the fastest method.
Step 2
Why this answer is correct
The correct answer is C. (30). \(\frac{6!}{4!}=6\times5=30\). Cancelling the common factorial part is the fastest method.
Step 3
Exam Tip
\(\frac{6!}{4!}=6\times5=30\)। समान फैक्टोरियल भाग को काटना सबसे तेज तरीका है।
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(1!+3!) का मान क्या होगा?
What is the value of (1!+3!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (7)
B (6)
C (4)
D (9)
Explanation opens after your attempt
Step 1
Concept
(1!=1) and (3!=6), so the sum is (7). Find small factorials separately first.
Step 2
Why this answer is correct
The correct answer is A. (7). (1!=1) and (3!=6), so the sum is (7). Find small factorials separately first.
Step 3
Exam Tip
(1!=1) और (3!=6), इसलिए योग (7) है। छोटे फैक्टोरियल पहले अलग-अलग निकालें।
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(0!) का मान कितना माना जाता है?
What is the value of (0!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (0)
B परिभाषित नहीं / Not defined
C (1)
D (10)
Explanation opens after your attempt
Step 1
Concept
In mathematics, (0!) is defined as (1). It is very useful in permutation and combination formulas.
Step 2
Why this answer is correct
The correct answer is C. (1). In mathematics, (0!) is defined as (1). It is very useful in permutation and combination formulas.
Step 3
Exam Tip
गणित में (0!=1) परिभाषित किया जाता है। यह संयोजन और क्रमचय सूत्रों में बहुत उपयोगी है।
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(5!) का मान क्या है?
What is the value of (5!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (100)
B (120)
C (60)
D (25)
Explanation opens after your attempt
Step 1
Concept
\(5!=5\times4\times3\times2\times1=120\). In factorial notation, multiply the number down to (1).
Step 2
Why this answer is correct
The correct answer is B. (120). \(5!=5\times4\times3\times2\times1=120\). In factorial notation, multiply the number down to (1).
Step 3
Exam Tip
\(5!=5\times4\times3\times2\times1=120\)। फैक्टोरियल में संख्या से (1) तक गुणा करते हैं।
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एक डिलीवरी कोड में पहले (3) स्थानों पर (8) उपलब्ध अक्षरों में से अलग-अलग अक्षर और अंतिम (3) स्थानों पर अंक (0) से (9) तक लिखे जाते हैं। यदि अंतिम (3) अंकों में ठीक (1) बार (0) आना चाहिए, तो कुल कोड कितने होंगे?
In a delivery code, the first (3) positions contain distinct letters chosen from (8) available letters and the last (3) positions contain digits from (0) to (9). If exactly one (0) must appear in the last (3) digits, how many codes are possible?
#permutations
#combinations
#counting_principle
#class_11
#expert
A \(8\cdot7\cdot6\cdot3\cdot9^2\)
B \(8\cdot7\cdot6\cdot10^3\)
C \(8^3\cdot3\cdot9^2\)
D \(8\cdot7\cdot6\cdot9^3\)
Explanation opens after your attempt
Correct Answer
A. \(8\cdot7\cdot6\cdot3\cdot9^2\)
Step 1
Concept
The letters can be chosen in \(8\times7\times6\) ways and the position of (0) can be chosen in (3) ways. The remaining two digits have \(9^2\) choices.
Step 2
Why this answer is correct
The correct answer is A. \(8\cdot7\cdot6\cdot3\cdot9^2\). The letters can be chosen in \(8\times7\times6\) ways and the position of (0) can be chosen in (3) ways. The remaining two digits have \(9^2\) choices.
Step 3
Exam Tip
अक्षरों के लिए \(8\times7\times6\) तरीके हैं और (0) का स्थान (3) तरीकों से चुनेगा। बाकी दो अंकों के लिए \(9^2\) विकल्प हैं।
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एक खेल टूर्नामेंट में (6) खिलाड़ियों में से स्वर्ण, रजत और कांस्य पदक विजेता चुने जाने हैं। यदि खिलाड़ी (A) को कोई पदक नहीं मिलना चाहिए, तो कुल परिणाम कितने हैं?
In a sports tournament, gold, silver, and bronze medal winners are to be chosen from (6) players. If player (A) must not receive any medal, how many outcomes are possible?
#permutations
#combinations
#counting_principle
#class_11
#expert
A (60)
B (120)
C (80)
D (100)
Explanation opens after your attempt
Step 1
Concept
After excluding player (A), (5) players remain and medals are ordered distinct positions. The outcomes are \(5\times4\times3=60\).
Step 2
Why this answer is correct
The correct answer is A. (60). After excluding player (A), (5) players remain and medals are ordered distinct positions. The outcomes are \(5\times4\times3=60\).
Step 3
Exam Tip
खिलाड़ी (A) को हटाने पर (5) खिलाड़ी बचते हैं और पदक क्रम में अलग हैं। परिणाम \(5\times4\times3=60\) हैं।
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