If ^nC_r denotes the number of combinations of n things taken r at a time, then the expression ^nC_r+1 + ^nC_r-1 + 2 × ^nC_r equals: - Mathematics MCQ AIEEE-CBSE-ENG-03 2026 | ExamTest.live

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If^{n} C_{r} denotes the number of combinations of n things taken r at a time, then the expression^{n} C_{r + 1} +^{n} C_{r - 1} + 2 \times^{n} C_{r} equals:

Solution & Step-by-step Explanation

The expression is:^{n} C_{r + 1} +^{n} C_{r} +^{n} C_{r} +^{n} C_{r - 1} Using the identity^{n} C_{k} +^{n} C_{k - 1} =^{n + 1} C_{k} : (^{n} C_{r + 1} +^{n} C_{r}) + (^{n} C_{r} +^{n} C_{r - 1}) =^{n + 1} C_{r + 1} +^{n + 1} C_{r} Using the identity again: =^{n + 2} C_{r + 1}

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If^{n} C_{r} denotes the number of combinations of n things taken r at a time, then the expression^{n} C_{r + 1} +^{n} C_{r - 1} + 2 \times^{n} C_{r} equals:

^{n + 2} C_{r}

^{n + 2} C_{r + 1}

^{n + 1} C_{r}

^{n + 1} C_{r + 1}

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