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NDA 1 2025 Maths, question 109

Topic: Probability

Passage · Q109 to Q110

A committee of 6 members is formed from a group of 7 gentlemen and 4 ladies.

Q109

What is the probability that the committee includes exactly 3 gentlemen?

  1. (a) 10/33Correct answer
  2. (b) 30/77
  3. (c) 100/231
  4. (d) 5/11

Solution.

Answer: (a) 10/33

  1. Assume all six-person committees are equally likely.
  2. There are (116)=462\binom{11}{6} = 462 committees.
  3. Exactly three gentlemen means three ladies too, so favourable committees number (73)(43)=35×4=140\binom{7}{3}\binom{4}{3} = 35 \times 4 = 140.
  4. The probability is 140/462=10/33140/462 = 10/33.