Question

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.

Answer 1

Answer

Step-by-step explanation:

Please feel free to ask anything you do not understand in the attachment.

Thankyou!

Answer 2

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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