Four persons are to be chosen at random from a group of 3 men. 2 women and 4 children. Find the probability of selecting
1. 1 man. 1 woman and 2 children
2. Exactly 2 children.
3. 2 women.
Answers
Answer
Step-by-step explanation:
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Probability of selecting 1. 1 man. 1 woman and 2 children = 2/7 & Exactly 2 children = 10/21 & 2 women = 1/6
Step-by-step explanation:
Four persons are to be chosen at random from a group of 3 men. 2 women and 4 children
Total 3 + 2 + 4 = 9
4 Can be selected out of 9 in ⁹C₄ ways
= 9!/(4!*5!)
= 126
1. 1 man. 1 woman and 2 children
=> ³C₁ * ²C₁ * ⁴C₂ = 3 * 2 * 6 = 36 Ways
Probability = 36/126 = 2/7
2. Exactly 2 children.
=> ⁵C₂ * ⁴C₂ = 10 * 6 = 60
Probability = 60/126 = 10/21
3. 2 women.
=> ²C₂ * ⁷C₂ = 1 * 21
Probability = 21/126 = 1/6
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