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Question
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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Solution
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 `""^12C_7` ways.
Thus, by multiplication principle, required number of ways of selecting cricket team
= 5C4 x 12C7 = `(5!)/(4! xx 1!) xx (12!)/(7! xx 5!)`
= `5/1 xx (12 xx 11 xx 10 xx 9 xx 8)/(1 xx 2 xx 3 xx 4 xx5)`
= 3960
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