CAT (QA) PYQs

The number of all positive integers up to $500$ with non-repeating digits is

The number of ways of distributing $20$ identical balloons among $4$ children such that each child gets some balloons but no child gets an odd number of balloons, is

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