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

The number of ways in which $21$ identical apples can be distributed among three children such that each child gets at least $2$ apples, is

If $^n{C_r} = 84,{\;^n}{C_{r - 1}} = 36$ and $^n{C_{r + 1}} = 126$, then $n$ equals

In how many ways can a girl and a boy be selected from a group of $15$ boys and $8 $ girls

If ${ }^{n} P_{r}={ }^{n} P_{r+1}$ and ${ }^{n} C_{r}={ }^{n} C_{r-1}$, then the value of $r$ is equal to:

If $^n{C_3} + {\,^n}{C_4} > {\,^{n + 1}}{C_3},$ then