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

Let $AB, CD, EF, GH,$ and $JK$ be five diameters of a circle with center at $O$. In how many ways can three points be chosen out of $A, B, C, D, E, F, G, H, J, K,$ and $O$ so as to form a triangle?