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

The number of $5$ card combinations out of a deck of $52$ cards such that there is exactly one ace in each combination is:

In how many ways can a committee of $5$ members be formed from $4$ gentlemen and $6$ ladies such that the number of gentlemen is greater than the number of ladies?

There are two urns. Urn $A$ has $3$ distinct red balls and urn $B$ has $9$ distinct blue balls. From each urn,two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

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

In how many ways can one girl and one boy be selected from a group of $15$ boys and $8$ girls?