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Question

Find the numbers of ways of selecting a cricket team of 11 players from 7 batsman and 6 bowlers such that there will be atleast 5 bowlers in the team.

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Solution

There should be atleast 5 bowlers, acc. to question

So, possible ways are,

$⟹$ (5 bowlers + 6 batsmen) and (6 bowlers + 5 batsmen)

$⟹ (^{6} C_{5} \times^{7} C_{6}) + (^{6} C_{6} \times^{7} C_{5})$

$⟹ 42 + 21 = 63$

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