Question
A football team of 11 players is to be formed from 20
players including 5 defenders and 4 goal keepers. In how many different ways can a team be formed so that the team contains exactly 2 goal keepers and at least 3 defenders?Solution
Total number of Defenders = 5 Total number of Goal keepers = 4 Total number of Normal players = 11 [20- (5+4)] Possible Combinations : ∴ Required Number of ways = (5C3 × 4C2 × 11C6) + (5C4 × 4C2 × 11C5) + (5C5 × 4C2 × 11C4) = 5!/(3! ×2!) × 4!/(2! ×2!) × 11!/(6! ×5!) + 5!/4! × 4!/(2! ×2!) × 11!/(5! ×6!) + 5!/5! × 4!/(2! ×2!) × 11!/(4! ×7!) = 10 × 6 × 462 + 5 × 6 × 462 + 1 × 6 × 330 = 27720 + 13860 + 1980 = 43560
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