# 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 - Mathematics

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?

#### Solution

A sports team of 11 students is to be constituted, choosing at least 5 students of class XI and at least 5 from class XII.
Required number of ways =${}^{20} C_5 \times^{20} C_6 + {}^{20} C_6 \times^{20} C_5 = 2 \times^{20} C_5 \times^{20} C_6 = 2 \left( {20}_{C_6} \times {20}_{C_5} \right)$

Concept: Combination
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.2 | Q 10 | Page 16

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