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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

Total number of students is XI = 20

Total number of students is XII = 20

Total number of students to be selected in c team = 11

(at least 5 from XI and 5 from XII)

this can be done in following ways

20C5×20C6+20C6×20C5=2(20C6×20C5)=(20!6!14!×20!5!15!)=2×20×19×18×17×16×15×20×19×18×17×166×5×4×3×2×5×4×3×2×1=19×17×16×15×2×19×3×17×8
= 120 1870080 ways


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