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Among 14 Players, 5 Are Bowlers. in How Many Ways a Team of 11 May Be Formed with at Least 4 Bowlers? (A) 265 (B) 263 (C) 264 (D) 275 - Mathematics

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MCQ

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.

\[\therefore \text{Required number of ways} = \ ^{5}{}{C}_4 \times \ ^{9}{}{C}_7 + \ ^{5}{}{C}_5 \times \ ^{9}{}{C}_6 \]
\[ = 180 + 84 \]
\[ = 264\]

Concept: Combination
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Q 24 | Page 26

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