$n$ balls each of weight $w$. When weighed in pairs,the sum of the weights of all possible pairs is $120$. When they are weighed in triplets,the sum of the weights of all possible triplets is $480$. Then $n$ is:

$A$ linguistic club of a certain Institute consists of $6$ girls and $4$ boys. $A$ team of $4$ members is to be selected from this group,including the selection of a Captain (from among these $4$ members) for the team. If the team has to include at most one boy,the number of ways of selecting the team is:

The number of ways in which $17$ apples can be distributed among $4$ guests such that each guest gets at least $3$ apples is

$A$ man has $10$ friends. In how many ways can he invite one or more of them to a party?

If $\binom{n+1}{3} = 2 \times \binom{n}{2}$,then $n = \dots$

The value of ${ }^{16} C_{9}+{ }^{16} C_{10}-{ }^{16} C_{6}-{ }^{16} C_{7}$ is