Value of 2^k (n 0) (n k) - 2^k-1 (n 1) (n-1 k-1) + 2^k-2 (n 2) (n-2 k-2) - ...... + (-1)^k (n k) (n-k 0) is

Question

Value of \(2^k\binom n0 \binom nk - 2^{k-1} \binom n1 \binom{n-1}{k-1} + 2^{k-2} \binom n2 \binom{n-2}{k-2}- .....+ (-1)^k \binom nk \binom{n-k}0\) is 

(a) \(\binom nk\)

(b) \(\binom{n-1}{k-1}\)

(c) 1

(d) None of these

Answer 1

Correct option is (a) \(\binom nk\)