Question

A sports team of 11 students is to be constituted, choosing at least 5 from Class XI and atleast 5 from Class XII. If there are 20 students in each of these classes, in how many ways can the team be constituted?

Answer 1

Total number of students in each class = 20

We have to select at least 5 students from each class.

So we can select either 5 students from class XI and 6 students from class XII or 6 students from class XI and 5 students from class XII.

∴ Total number of ways of selecting a team of 11 players = 20C5 x 20C6 + 20C6 x 20C5 = 2 x 20C5 x 20C6