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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?
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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 =\[{}^{20} C_5 \times^{20} C_6 + {}^{20} C_6 \times^{20} C_5 = 2 \times^{20} C_5 \times^{20} C_6 = 2 \left( {20}_{C_6} \times {20}_{C_5} \right)\]
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