CAT (QA) PYQs

A four-digit number is formed by using only the digits $1$, $2$ and $3$ such that both $2$ and $3$ appear at least once. The number of all such four-digit numbers is

The number of ways of distributing $15$ identical balloons, $6$ identical pencils and $3$ identical erasers among $3$ children, such that each child gets at least four balloons and one pencil, is

In how many ways can $8$ identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least $1$ pen, Bimal gets at least $2$ pens, and Kamal gets at least $3$ pens?