(10) खिलाड़ियों में से (5) चुनने हैं और दो विशेष खिलाड़ी साथ में नहीं चुने जाने चाहिए। कितने तरीके हैं?

From (10) players, (5) are to be selected and two special players should not be selected together. How many ways are there?

Explanation opens after your attempt
Correct Answer

B. (224)

Step 1

Concept

Total ways are \(\binom{10}{5}=252\), and ways with both special players are \(\binom{8}{3}=56\). Thus the valid ways are (196).

Step 2

Why this answer is correct

The correct answer is B. (224). Total ways are \(\binom{10}{5}=252\), and ways with both special players are \(\binom{8}{3}=56\). Thus the valid ways are (196).

Step 3

Exam Tip

कुल \(\binom{10}{5}=252\) और दोनों विशेष साथ हों तो \(\binom{8}{3}=56\) तरीके हैं। इसलिए (252-56=196) नहीं बल्कि सही बचा (196) है।

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Mathematics Answer, Explanation and Revision Hints

(10) खिलाड़ियों में से (5) चुनने हैं और दो विशेष खिलाड़ी साथ में नहीं चुने जाने चाहिए। कितने तरीके हैं? / From (10) players, (5) are to be selected and two special players should not be selected together. How many ways are there?

Correct Answer: B. (224). Explanation: कुल \(\binom{10}{5}=252\) और दोनों विशेष साथ हों तो \(\binom{8}{3}=56\) तरीके हैं। इसलिए (252-56=196) नहीं बल्कि सही बचा (196) है। / Total ways are \(\binom{10}{5}=252\), and ways with both special players are \(\binom{8}{3}=56\). Thus the valid ways are (196).

Which concept should I revise for this Mathematics MCQ?

Total ways are \(\binom{10}{5}=252\), and ways with both special players are \(\binom{8}{3}=56\). Thus the valid ways are (196).

What exam hint can help solve this Mathematics question?

कुल \(\binom{10}{5}=252\) और दोनों विशेष साथ हों तो \(\binom{8}{3}=56\) तरीके हैं। इसलिए (252-56=196) नहीं बल्कि सही बचा (196) है।