Class 11 Mathematics Permutations and Combinations Derivations of formulas and their connections Expert Level 64

\(\sum_{r=0}^{n}{}^{n}C_r{}^{r}C_k\) का simplified form कौन-सा है?

What is the simplified form of \(\sum_{r=0}^{n}{}^{n}C_r{}^{r}C_k\)?

Explanation opens after your attempt
Correct Answer

A. \(^{n}C_k2^{n-k}\)

Step 1

Concept

Choose the (k) marked members first, then each of the remaining (n-k) members may or may not enter the subset. In exams choose the marked set first in nested selection.

Step 2

Why this answer is correct

The correct answer is A. \(^{n}C_k2^{n-k}\). Choose the (k) marked members first, then each of the remaining (n-k) members may or may not enter the subset. In exams choose the marked set first in nested selection.

Step 3

Exam Tip

पहले (k) marked members चुनें, फिर बाकी (n-k) members subset में आएं या न आएं। परीक्षा में nested selection में marked set पहले चुनें।

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\(\sum_{r=0}^{n}{}^{n}C_r{}^{r}C_k\) का simplified form कौन-सा है? / What is the simplified form of \(\sum_{r=0}^{n}{}^{n}C_r{}^{r}C_k\)?

Correct Answer: A. \(^{n}C_k2^{n-k}\). Explanation: पहले (k) marked members चुनें, फिर बाकी (n-k) members subset में आएं या न आएं। परीक्षा में nested selection में marked set पहले चुनें। / Choose the (k) marked members first, then each of the remaining (n-k) members may or may not enter the subset. In exams choose the marked set first in nested selection.

Which concept should I revise for this Mathematics MCQ?

Choose the (k) marked members first, then each of the remaining (n-k) members may or may not enter the subset. In exams choose the marked set first in nested selection.

What exam hint can help solve this Mathematics question?

पहले (k) marked members चुनें, फिर बाकी (n-k) members subset में आएं या न आएं। परीक्षा में nested selection में marked set पहले चुनें।