In how many ways can one select a cricket tea | vedclass

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Question

(A) Total players = $17$. Number of bowlers = $5$. Number of non-bowlers = $17 - 5 = 12$.We need to select a team of $11$ players including exactly $4

Vedclass · Accepted Answer

$3960$

Vedclass · Answer

(A) Total players = $17$. Number of bowlers = $5$. Number of non-bowlers = $17 - 5 = 12$.We need to select a team of $11$ players including exactly $4$ bowlers.Number of ways to select $4$ bowlers from $5$ is $^{5}C_{4} = \frac{5!}{4!1!} = 5$.Number of ways to select the remaining $11 - 4 = 7$ players from $12$ non-bowlers is $^{12}C_{7} = \frac{12!}{7!5!} = \frac{12 	imes 11 	imes 10 	imes 9 	imes 8}{5 	imes 4 	imes 3 	imes 2 	imes 1} = 792$.Total number of ways = $^{5}C_{4} 	imes ^{12}C_{7} = 5 	imes 792 = 3960$.

In how many ways can one select a cricket team of $11$ 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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