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 atleast 5 students from each class.

We have the following cases:

(i) 5 students from XI class and 6 students from XII class

(ii) 6 students from XI class and 5 students from XII class

So, number of ways of selection of a team of 11 players

= ²⁰C₅ × ²⁰C₆ + ²⁰C₆ × ²⁰C₅ ......[²⁰C₅ ×  ²⁰C₆]

Hence, the required ways of selection = 2[²⁰C₅ ×  ²⁰C₆]