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In how many ways can one select a cricke...

In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?

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Number of ways of selecting 4 bowlers out of 5
`.^(5)C_(4)=.^(5)C_((5-4))=.^(5)C_(1)=5`.
Number of ways of selecting 7 batsmen out of 12
`=.^(12)C_(7)=.^(12)C_((12-7))=.^(12)C_(5)=(12xx11xx10xx9xx8)/(5xx4xx3xx2xx1)=792`.
Hence, the number of ways of selecting the team `=(5xx792)=3960`.
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