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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?



Answer -

Given:

Total number ofstudents in XI = 20

Total number ofstudents in XII = 20

Total number ofstudents to be selected in a team = 11 (with atleast 5 from class XI and 5 fromclass XII)

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 classXII)

= (20C6 × 20C5)+ (20C5 × 20C6)

= 2 (20C6 × 20C5)ways

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