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Four persons are to be chosen from a group of 3 men, 2 women and 4 children. Find the probability of choosing exactly 2 women. 
  • a)
    3/50 
  • b)
     12/25 
  • c)
    1/5 
  • d)
     1/6 
  • e)
     1/7
Correct answer is option 'D'. Can you explain this answer?
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Four persons are to be chosen from a group of 3 men, 2 women and 4 chi...
Problem: Four persons are to be chosen from a group of 3 men, 2 women, and 4 children. Find the probability of choosing exactly 2 women.

Solution:

Total number of ways to choose 4 persons out of 3 men, 2 women, and 4 children = 9C4
= (9 × 8 × 7 × 6)/(4 × 3 × 2 × 1) = 126

Number of ways to choose 2 women out of 2 women and 7 non-women = 2C2 × 7C2
= (1 × 21)/2 = 21/2

Number of ways to choose 2 persons out of 4 persons = 4C2
= (4 × 3)/(2 × 1) = 6

Therefore, the number of ways to choose exactly 2 women and 2 others = (2C2 × 7C2) × (4C2) = 21 × 6 = 126

Hence, the probability of choosing exactly 2 women =
(number of ways to choose exactly 2 women and 2 others) / (total number of ways to choose 4 persons)
= 126/126 = 1

Therefore, the correct option is D.
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