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

If seven women and seven men are to be seated around a circular table such that there is a man on either side of every woman,then the number of seating arrangements is

$A$ 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

How many different nine-digit numbers can be formed from the digits of the number $223355888$ by rearranging the digits so that the odd digits occupy even places?

How many numbers lying between $1000$ and $10000$ can be formed by using the digits $1, 3, 5, 6, 7, 8, 9$ if no digits are repeated?

Let $n(A) = 3$ and $n(B) = 3$ (where $n(S)$ denotes the number of elements in set $S$). Then,the number of subsets of $(A \times B)$ having an odd number of elements is: