Permutation and Combination: If ^nC_r denotes the number of combinations of n things taken r at a… | AIEEE 2003

AIEEE 2003 (Offline)Question 1

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

Permutation and Combination

${}^{n+1}C_{r+1}$${}^{n+2}C_{r}$${}^{n+2}C_{r+1}$✓ Correct answer${}^{n+1}C_{r}$

Solution

${}^nC_{r+1}+{}^nC_r+{}^nC_r+{}^nC_{r-1}={}^{n+1}C_{r+1}+{}^{n+1}C_r={}^{n+2}C_{r+1}$.

Permutation and Combination - JEE Mathematics question (AIEEE 2003 (Offline))

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