The number of seven digit positive integers formed using the digits $1,2,3$ and $4$ only and sum of the digits equal to $12$ is $...........$.

The number of ways in which an examiner can assign $30$ marks to $8$ questions, giving not less than $2$ marks to any question, is

If $'n'$ objects are arranged in a row then the number of ways of selecting three of these objects so that no two of them are next to each othe

A student is allowed to select at most $n$ books from a collection of $(2n + 1)$ books. If the total number of ways in which he can select one book is $63$, then the value of $n$ is

The number of ways in which five identical balls can be distributed among ten identical boxes such that no box contains more than one ball, is

There are three bags $B_1$,$B_2$ and $B_3$ containing $2$ Red and $3$ White, $5$ Red and $5$ White, $3$ Red and $2$ White balls respectively. A ball is drawn from bag $B_1$ and placed in bag $B_2$, then a ball is drawn from bag $B_2$ and placed in bag $B_3$, then a ball is drawn from bag $B_3$. The number of ways in which this process can be completed, if same colour balls are used in first and second transfers (Assume all balls to be different) is