In how many ways can $35$ apples be distributed among $3$ boys such that each boy can have any number of apples?

The English alphabet has $5$ vowels and $21$ consonants. How many words with $2$ different vowels and $2$ different consonants can be formed from the alphabet?

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

Statement-$1:$ The number of ways of distributing $10$ identical balls in $4$ distinct boxes such that no box is empty is $^9C_3$.
Statement-$2:$ The number of ways of choosing any $3$ places from $9$ different places is $^9C_3$.

In how many ways can a committee of $6$ members be formed from $8$ men and $4$ women such that the committee contains at least $3$ women?

If $^nC_{12} = ^nC_6$,then $^nC_2 = $