If $^{n^2 - n}C_2 = ^{n^2 - n}C_{10}$,then $n = $

The number of ways five alphabets can be chosen from the alphabets of the word $MATHEMATICS$,where the chosen alphabets are not necessarily distinct,is equal to :

The total number of ways of selecting $4$ letters from all the letters of the word $TSEAMCET$ is

If there are $6$ alike fruits,$7$ alike vegetables,and $8$ alike biscuits,then the number of ways of selecting any number of things out of them such that at least one from each category is selected,is

Let the number of elements in sets $A$ and $B$ be $5$ and $2$ respectively. Then the number of subsets of $A \times B$ each having at least $3$ and at most $6$ elements is:

From a group of $10$ men and $8$ women,the number of ways of forming a committee of $8$ members with not more than $5$ men and not less than $5$ women is