IPMAT Rohtak 2020 (QA) PYQs

Out of 13 objects, 4 are indistinguishable and the rest are distinct. The number of ways we can choose 4 objects out of 13 objects is __________.

A box contains 2 white shirts, 3 black shirts, and 4 red shirts. In how many ways can 3 shirts be drawn from the box, if at least one black shirt is to be included in the draw?

Let $n$ be the number of ways in which 20 identical balloons can be distributed among 5 girls and 3 boys such that everyone gets at least one balloon and no girl gets fewer balloons than a boy does. Then