Permutations and Combinations · Class 11 · CBSE · Science Mathematics

A committee of 3 members is to be selected from 5 boys and 4 girls. How many committees will contain at least one girl?

Practice question from Permutations and Combinations (Class 11 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.

medium · MCQ · Q-5AD93F

A committee of 3 members is to be selected from 5 boys and 4 girls. How many committees will contain at least one girl?

  1. A.50
  2. B.60
  3. C.74Correct answer
  4. D.84

Solution

Total committees are 9C3=84{}^{9}C_{3}=84. Committees containing no girl are 5C3=10{}^{5}C_{3}=10. Hence, committees with at least one girl are 84−10=7484-10=74.

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