Question

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

Answer 1

Given as

The total number of students in XI = 20

The total number of students in XII = 20

The total number of students to be selected in a team = 11 (with atleast 5 from class XI and 5 from class XII)

The number of ways = (No. of ways of selecting 6 students from class XI and 5 students from class XII) + (No. of ways of selecting 5 students from class XI and 6 students from class XII)

= (²⁰C₆ × ²⁰C₅) + (²⁰C₅ × ²⁰C₆)

= 2 (²⁰C₆ × ²⁰C₅) ways