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:

The number of non-negative integral solutions of the equation $x+y+z+t=10$ when $x \geq 2$ and $z \geq 5$ is:

The number of ways in which $15$ identical gold coins can be distributed among $3$ persons such that each one gets at least $3$ gold coins is

The number of ways in which $3$ identical balls can be distributed into $7$ distinct bins is

$A$ student is allowed to select at least $(n+1)$ books but not all books from a collection of $(2n+1)$ books. If the total number of ways in which he can select these books is $255$,then the number of books in that collection is