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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Permutation and Combination

NDA 2018 · Mathematics · Permutation and Combination

There are 17 cricket players, out of which 5 players can bowl. In...

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?

Options

  1. AC(17,11)\mathrm{C}(17,11)
  2. BC(12,8)\mathrm{C}(12,8)
  3. CC(17,5)×(5,3)\mathrm{C}(17,5) \times(5,3)
  4. DC(5,3)×C(12,8)\mathrm{C}(5,3) \times \mathrm{C}(12,8)

Correct answer

D. C(5,3)×C(12,8)\mathrm{C}(5,3) \times \mathrm{C}(12,8)

Step-by-step solution

3 bowlers are selected among 5 bowlers in 5C3{ }^5 \mathrm{C}_3 ways. Remaining 8 player's are selected from 12 player's in 12C8{ }^{12} \mathrm{C}_8 ways. ∴\therefore total number of ways =12C8×5C3={ }^{12} \mathrm{C}_8 \times{ }^5 \mathrm{C}_3.
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