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

If a polygon has $44$ diagonals,then the number of its sides are

How many numbers consisting of $5$ digits can be formed in which the digits $3, 4$ and $7$ are used only once and the digit $5$ is used twice?

How many $3$-digit even numbers can be formed using the digits $0, 2, 3, 5, 7$ when repetition is not allowed?

$A$ committee of $12$ is to be formed from $9$ women and $8$ men in which at least $5$ women have to be included in a committee. Then the number of committees in which the women are in majority and men are in majority are respectively

In how many ways can $6$ letters be posted in $5$ letter boxes available in the locality?