$A$ 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 number of elements in the set $\{x \in N : ^{20-2x}C_{x-3} \in N\}$ is

If $10 \cdot ^nC_2 = 3 \cdot ^{n+1}C_3$,then the value of $n$ is

If ${ }^{15} C_4+{ }^{15} C_5+{ }^{16} C_6+{ }^{17} C_7+{ }^{18} C_8={ }^{19} C_{r}$,then the value of $r$ is equal to

$A$ student is allowed to choose at most $n$ books from a collection of $2n+1$ books. If the total number of ways in which he can select at least one book is $255$,then the value of $n$ is:

$A$ man has $7$ friends. In how many ways can he invite one or more of them for a tea party?