$A$ group consists of $4$ girls and $7$ boys. In how many ways can a team of $5$ members be selected if the team has no girl?

The total number of $3$-digit numbers,whose sum of digits is $10$,is

$A$ question paper consists of two sections having $3$ and $4$ questions respectively. The following note is given on the paper: "It is not necessary to attempt all the questions. One question from each section is compulsory". In how many ways can a candidate select the questions?

If $^{n}C_{8} = ^{n}C_{2}$,find $^{n}C_{2}$.

The value of $r$ for which $^{20}C_r ^{20}C_0 + ^{20}C_{r-1} ^{20}C_1 + ^{20}C_{r-2} ^{20}C_2 + ... + ^{20}C_0 ^{20}C_r$ is maximum is

The number of ways in which $3$ identical balls can be distributed into $7$ distinct bins is