Permutations And Combinations Ques 37
- Let $S={1,2,3, \ldots \ldots, 9}$. For $k=1,2, \ldots \ldots .5$, let $N _k$ be the number of subsets of $S$, each containing five elements out of which exactly $k$ are odd. Then $N _1+N _2+N _3+N _4+N _5=\quad$ (2017 Adv.)
210
252
126
125
Show Answer
Answer:
Correct Answer: 37.(c)
Solution:
Formula:
Combinations under restrictions:
$N _i={ }^{5} C _k \times{ }^{4} C _{k}$
$$ \begin{aligned} & N _1=5 \times 10^0 \\ & N_2=10 \times 4 \ & N_3=10 \times 6 \ & N_4=5 \times 4 \ & N _5=1 \ & N _1+N _2+N _3+N _4+N _5=126 \end{aligned} $$
BETA
