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# 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?

Q.7.     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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Out off, 17 players, 5 are bowlers.

A cricket team of 11 is to be selected such that there are exactly 4 bowlers.

4 bowlers can be selected in $^5C_4$  ways and 7 players can be selected in $^1^2C_7$ ways.

Thus, using multiplication priciple, number of ways of selecting the team $=^5C_4 .^1^2C_7$

$=\frac{5!}{1!4!}\times \frac{12!}{5!7!}$

$=5 \times \frac{12\times 11\times 10\times 9\times 8}{5\times 4\times 3\times 2}$

$=3960$

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