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

Let $A$ and $B$ be two sets containing $4$ and $2$ elements respectively. Then the number of subsets of the set $A \times B$,each having at least $3$ elements is:

Find the total number of $9$ digit numbers which have all the digits different.

The number of ways in which a committee of $6$ members can be formed from $8$ gentlemen and $4$ ladies so that the committee contains at least $3$ ladies is:

$A$ person is permitted to select at least one and at most $n$ coins from a collection of $(2n + 1)$ distinct coins. If the total number of ways in which he can select coins is $255$,then $n$ equals

If ${}^n{P_5} = 20 \cdot {}^n{P_3}$,then $n = $