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

What is the number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these are all $4$ cards face cards?

$A$ committee of $5$ is to be formed out of $6$ men and $4$ ladies. The number of ways this can be done,when at most $2$ ladies are included,is

$^{n-1}C_r = (k^2 - 8) ^nC_{r+1}$ if and only if:

The least value of natural number $n$ satisfying $C(n, 5) + C(n, 6) > C(n + 1, 5)$ is

There are two urns. Urn $A$ contains $3$ distinct red balls,and Urn $B$ contains $9$ blue balls. If two balls are selected at random from each urn and swapped,in how many ways can this operation be performed?