Question

Let S = {1, 2, 3,………,9}. For k = 1, 2, ……..5, let $N_k$ be the number of subsets of S, each containing five elements out of which exactly k are odd. Then $N_1+N_2+N_3+N_4+N_5=$

• A. 210
• B. 252
• C. 126
• D. 125

Answer 1

The correct option is C 126

$N_i{=}^5{C}_k{\times }^4{C}_{5-k}{N}_1=5\times 1N_2=10\times 4N_3=10\times 6N_4=5\times 4N_5=1N_1+N_2+N_3+N_4+N_5=126$