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  4. In a group of 13 cricket players, four are bowlers. Find out in how many ways can they form a cricket team of 11 players in which at least 2 bowlers are included.

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Q. In a group of $13$ cricket players, four are bowlers. Find out in how many ways can they form a cricket team of $11$ players in which at least $2$ bowlers are included.

Permutations and Combinations

Solution:

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$\Rightarrow{ }^{4} C _{2} \times{ }^{9} C _{9}+{ }^{4} C _{3} \times{ }^{9} C _{8}+{ }^{4} C _{4} \times{ }^{9} C _{7}$
$=6+36+36=78$