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Question
In how many ways can one select a cricket team of eleven from 17 players in which only 5 persons can bowl if each cricket team of 11 must include exactly 4 bowlers?
Solution
Out of 17 players, 11 need to be selected. There are 5 bowlers, of which four must be selected in the team. So, we have to choose 7 players from the remaining 12 players.
Required number of ways =\[{}^5 C_4 \times^{12} C_7 = 5 \times \frac{12!}{7! 5!} = 5 \times 792 = 3960\]
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