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

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 $4$-digit numbers, each greater than $1000$ and each having all four digits distinct, are there with $7$ coming before 3?