यदि \(A=\{a,b,c,d,e,f,g\}\) है, तो \(\mathcal{P}(A)\) में (4) तत्वों वाले ऐसे subsets कितने हैं जिनमें (a) हो और (b) न हो?
If \(A=\{a,b,c,d,e,f,g\}\), how many (4)-element subsets in \(\mathcal{P}(A)\) contain (a) and do not contain (b)?
Explanation opens after your attempt
Correct Answer
A. (10)
Concept
(a) is fixed and (b) is excluded, so the remaining (3) elements must be chosen from (5) elements. The number is \(\binom{5}{3}=10\).
Why this answer is correct
The correct answer is A. (10). (a) is fixed and (b) is excluded, so the remaining (3) elements must be chosen from (5) elements. The number is \(\binom{5}{3}=10\).
Exam Tip
(a) fixed है और (b) excluded है, इसलिए बाकी (3) तत्व (5) तत्वों से चुनने होंगे। संख्या \(\binom{5}{3}=10\) है।
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