CAT (QA) PYQs

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

A cafeteria offers 5 types of sandwiches. Moreover, for each type of sandwich, a customer can choose one of 4 breads and opt for either small or large sized sandwich. Optionally, the customer may also add up to 2 out of 6 available sauces. The number of different ways in which an order can be placed for a sandwich, is

How many four digit numbers, which are divisible by $6$, can be formed using the digits $0, 2, 3, 4, 6$, such that no digit is used more than once and $0$ does not occur in the left-most position?