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Question
Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with at least 4 bowlers?
Options
265
263
264
275
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Solution
264
Among 14 players, 5 are bowlers.
A team of 11 players has to be selected such that at least 4 bowlers are included in the team.
\[\therefore \text{Required number of ways} = \ ^{5}{}{C}_4 \times \ ^{9}{}{C}_7 + \ ^{5}{}{C}_5 \times \ ^{9}{}{C}_6 \]
\[ = 180 + 84 \]
\[ = 264\]
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