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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?
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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
$$\Rightarrow \displaystyle ^{5}C_4 \times ^{12}C_7=\frac {5!}{4!1!}\times \frac {12!}{7!5!}$$
$$=\displaystyle \frac {12\times 11\times 10\times 9\times 8}{5\times 4\times 3\times 2\times 1}\times 1$$
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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Question Text | 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? |
Answer Type | Text solution:1 |
Upvotes | 150 |