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There are 17 cricket players, out of which 5 players can bowl. In how many ways can a team of 11 players be selected so as to include 3 bowlers?
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The correct answer is:
$\mathrm{C}(5,3) \times \mathrm{C}(12,8)$
3 bowlers are selected among 5 bowlers in ${ }^{5} \mathrm{C}_{3}$ ways. Remaining 8 player's are selected from 12 player's in ${ }^{12} \mathrm{C}_{8}$ ways.
$\therefore$ total number of ways $={ }^{12} \mathrm{C}_{8} \times{ }^{5} \mathrm{C}_{3}$.
$\therefore$ total number of ways $={ }^{12} \mathrm{C}_{8} \times{ }^{5} \mathrm{C}_{3}$.
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