Mahesh has $6$ friends. In how many ways can he invite one or more friends for dinner?

$A$ student is to answer $10$ out of $13$ questions in an examination such that he must choose at least $4$ from the first $5$ questions. The number of choices available to him is

Out of $14$ cricket players,$5$ are bowlers. In how many ways can a team of $11$ players be selected such that the team contains at least $4$ bowlers?

If ${ }^9 C_3+{ }^9 C_5={ }^{10} C_r$ for some $r \in N$,then $r=$

In a football championship,there were played $153$ matches. Every team played one match with each other. The number of teams participating in the championship is

$\binom{n}{r} \div \binom{n}{n-1} = \dots$