In how many different ways can the letters of the word $ALLAHABAD$ be permuted?

There are $12$ members in a group. In how many ways can a team of $6$ members be selected such that a particular member is always included?

$A$ set contains $(2n + 1)$ elements. The number of subsets of the set which contain at most $n$ elements is:

$A$ 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 $5$ red and $4$ white balls be drawn from a bag containing $10$ red and $8$ white balls?

All possible two-factor products are formed from the numbers $1, 2, 3, 4, \dots, 200$. The number of products out of the total obtained which are multiples of $5$ is: