If $^{15}C_{3r} = ^{15}C_{r+3}$,then the value of $r$ is

$A$ village has $10$ players. $A$ team of $6$ players is to be formed. $5$ members are chosen out of these $10$ players and then the captain is chosen from the remaining $5$ players. The total number of ways of choosing such a team is:

If ${}^{2n}C_3 : {}^{n}C_3 = 10 : 1$,then the ratio $(n^2 + 3n) : (n^2 - 3n + 4)$ is

At an election,a voter may vote for any number of candidates not exceeding the number to be elected. If $4$ candidates are to be elected out of the $12$ contested in the election and a voter votes for at least one candidate,then the number of ways in which a voter can vote is:

In how many ways can a committee of $5$ members be formed from $4$ gentlemen and $6$ ladies such that the number of gentlemen is greater than the number of ladies?

The number of ways in which a team of $11$ players can be formed out of $25$ players,if $6$ out of them are always to be included and $5$ of them are always to be excluded,is