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NDA 1 2025 Maths, question 110

Topic: Probability

Passage · Q109 to Q110

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

Q110

What is the probability that the committee includes at least 2 ladies?

  1. (a) 41/66
  2. (b) 47/66
  3. (c) 49/66
  4. (d) 53/66Correct answer

Solution.

Answer: (d) 53/66

  1. Use the complement: zero ladies gives (76)=7\binom{7}{6} = 7 committees; one lady gives (41)(75)=4×21=84\binom{4}{1}\binom{7}{5} = 4 \times 21 = 84.
  2. Thus the required probability is 1−(7+84)/462=371/462=53/661 - (7 + 84)/462 = 371/462 = 53/66.