Question

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

Answer 1

We know that,

A team of 11 students can be constituted in the following two ways

(i) 5 students from class XI and 6 students from XII = ²⁰C_5. ²⁰C₆

(ii) 6 students from class XI and 5 students from XII = ²⁰C_6.²⁰C₅

The number ways the team can be constituted = Case(i)+case(ii)

= ²⁰C_5. ²⁰C₆ + ²⁰C_6.²⁰C₅

= 2(²⁰C_5. ²⁰C₆)