The value of $^{15}C_{3} + ^{15}C_{13}$ is

The number of values of $r$ satisfying $^{69}C_{3r-1} - ^{69}C_{r^2} = ^{69}C_{r^2-1} - ^{69}C_{3r}$ is:

In an election,$3$ members are to be elected from $6$ candidates. $A$ voter can cast their vote for any number of candidates but not more than the number of candidates to be elected. In how many ways can a voter cast their vote?

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

In a conference of $8$ persons,if each person shakes hands with every other person exactly once,then the total number of handshakes is:

In a touring cricket team,there are $16$ players in all,including $5$ bowlers and $2$ wicket-keepers. How many teams of $11$ players can be chosen from these,such that the team includes exactly $3$ bowlers and $1$ wicket-keeper?