There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsman and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsman and 1 wicketkeeper, is ______________.
Answer (integer)
777
Solution
15 : Players<br><br>6 : Bowlers<br><br>7 : Batsman<br><br>2 : Wicket keepers<br><br>Total number of ways for :<br><br>at least 4 bowler, 5 batsman & 1 wicket keeper<br><br>= $${}^6{C_4}({}^7{C_6} \times {}^2{C_1} + {}^7{C_5} \times {}^2{C_2}) + {}^6{C_5} \times {}^7{C_5} \times {}^2{C_1}$$<br><br>$= 777$
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
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