Let $S=\{1,2,3, \ldots ., 9\}$. 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 $N_1+N_2+N_3+N_4+N_5=$

If the number of five digit numbers with distinct digits and $2$ at the $10^{\text {th }}$ place is $336 \mathrm{k}$, then $\mathrm{k}$ is equal to

In an election there are $5$ candidates and three vacancies. A voter can vote maximum to three candidates, then in how many ways can he vote

A boy needs to select five courses from $12$ available courses, out of which $5$ courses are language courses. If he can choose at most two language courses, then the number of ways he can choose five courses is

A committee of $7$ has to be formed from $9$ boys and $4$ girls. In how many ways can this be done when the committee consists of:

at least $3$ girls?

In a club election the number of contestants is one more than the number of maximum candidates for which a voter can vote. If the total number of ways in which a voter can vote be $62,$ then the number of candidates is :-