A class contains $b$ boys and $g$ girls. If the number of ways of selecting $3$ boys and $2$ girls from the class is $168$, then $b +3\,g$ is equal to.

If $2 \times {}^n{C_5} = 9\,\, \times \,\,{}^{n - 2}{C_5}$, then the value of $n$ will be

A student is allowed to select at most $n$ books from a collection of $(2n + 1)$ books. If the total number of ways in which he can select one book is $63$, then the value of $n$ is

To fill $12$ vacancies there are $25$ candidates of which five are from scheduled caste. If $3$ of the vacancies are reserved for scheduled caste candidates while the rest are open to all, then the number of ways in which the selection can be made

If $^n{C_r}$ denotes the number of combinations of $n$ things taken $r$ at a time, then the expression $^n{C_{r + 1}} + {\,^n}{C_{r - 1}} + \,2 \times {\,^n}{C_r}$ equals

Find the number of ways of selecting $9$ balls from $6$ red balls, $5$ white balls and $5$ blue balls if each selection consists of $3$ balls of each colour.