Permutation and CombinationHard
Question
Out of 16 players of a cricket team, 4 are bowlers and 2 are wicket keepers. A team of 11 players is to be chosen so as to contain at least 3 bowlers and at least 1 wicketkeeper. The number of ways in which the team be selected, is
Options
A.2400
B.2472
C.2500
D.960
Solution
Number of bowlers = 4
Number of wicketkeeper = 2
Let total number required selection
4C3 . 2C1 .10C7 + 4C4 .2C1 .10C6 + 4C3 . 2C2 .10C6 + 4C4 . 2C2 .10C5
960 + 420 + 840 + 252
= 2472
Number of wicketkeeper = 2
Let total number required selection
4C3 . 2C1 .10C7 + 4C4 .2C1 .10C6 + 4C3 . 2C2 .10C6 + 4C4 . 2C2 .10C5
960 + 420 + 840 + 252
= 2472
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