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 group of $9$ students, $s 1, s 2, \ldots, s 9$, is to be divided to form three teams $X, Y$ and, $Z$ of sizes $2,3$ , and $4$, respectively. Suppose that $s_1$ cannot be selected for the team $X$, and $s_2$ cannot be selected for the team $Y$. Then the number of ways to form such teams, is. . . .

What is the number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these

four cards are of the same suit,

If $^{15}{C_{3r}}{ = ^{15}}{C_{r + 3}}$, then the value of $r$ is

The least value of a natural number $n$ such that $\left(\frac{n-1}{5}\right)+\left(\frac{n-1}{6}\right) < \left(\frac{n}{7}\right)$, where $\left(\frac{n}{r}\right)=\frac{n !}{(n-r) ! r !}, i$

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?