A sports team of 11 students is to be constituted, choosing at least 5

1.	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» 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

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»

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

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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?

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