How many groups can be selected for playing football out of $5$ ladies and $4$ gentlemen such that there should be one lady and one gentleman on each side?

The number of different $6$-digit numbers that are divisible by $10$,which can be formed using the digits $1, 2, 7, 0, 9, 5$?

How many $4$-digit numbers,divisible by $5$,can be formed using the digits $0, 3, 5, 7,$ and $9$ if repetition of digits 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 a certain test,${a_i}$ students gave wrong answers to at least $i$ questions,where $i = 1, 2, 3, ..., k$. No student gave more than $k$ wrong answers. The total number of wrong answers given is:

$8$-digit numbers are formed using the digits $1, 1, 2, 2, 2, 3, 4, 4$. The number of such numbers in which the odd digits do not occupy odd places is: