List of top Mathematics Questions on Combinations asked in JEE Advanced

A group of 9 students, s₁, s₂,…., s₉, is to be divided to form three teams X, Y and Z of sizes 2, 3, and 4, respectively. Suppose that s₁ cannot be selected for the team X and s₂ cannot be selected for the team Y. Then the number of ways to form such teams, is _______.

The number of seven-digit integers, with sum of the digits equal to $10$ and formed by using the digits $1, 2$ and $3$ only, is