In how many ways can one select a cricket team of eleven from 17 p | Filo

Class 11

Math

Algebra

Permutations and Combinations

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

Solution: Given $$17$$ players , $$5$$ players are bowlers , so remaining $$12$$ are batsman.

A cricket team of $$11$$ players is to be selected in such a way that there are exactly $$4$$ bowlers.

$$4$$ bowlers can be selected in $$^5C_4$$ways and the remaining $$7$$ players can be selected out of the $$12$$ players in  $$^{12}C_7$$ ways.

Thus, by multiplication principle, required number of ways of selecting cricket team

$$\Rightarrow \displaystyle ^{5}C_4 \times ^{12}C_7=\frac {5!}{4!1!}\times \frac {12!}{7!5!}$$

$$=\displaystyle \frac {12\times 11\times 10\times 9\times 8}{5\times 4\times 3\times 2\times 1}\times 1$$

$$=3960$$
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