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?
Solution and Explanation
Out of 17 players, 5 players are bowlers.
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 \(^{12}C_7\)
Thus, by multiplication principle, required number of ways of selecting cricket team
\(=\) \(^5C_4\times\space^{12}C_7\)
\(=\frac{5!}{4!1!}\times\frac{12!}{7!5!}\)
\(=\frac{5\times12\times11\times10\times9\times8}{5\times4\times3\times2\times1}\)
\(=3960\)
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Permutations and Combinations
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Permutation is the method or the act of arranging members of a set into an order or a sequence.
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- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.