SOLUTION: A committee of seven people is to be selected from a group of 10 men and 8 women.What is the propability that the committee will be made of 2 men or 3 women ?

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Question 1104506: A committee of seven people is to be selected from a group of 10 men and 8 women.What is the propability that the committee will be made of 2 men or 3 women ?
Found 2 solutions by Edwin McCravy, rothauserc:
Answer by Edwin McCravy(20064)   (Show Source): You can put this solution on YOUR website!
This is worded badly.  Why?

A committee of 7 can't be made of 2 men only.  Who are the other 5?
Are they all women, or some men and some women?  That isn't clear.

A committee of 7 can't be made of 3 women only.  Who are the other 4?
Are they all men, or some men and some women?  That isn't clear.

Edwin
Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
There are 18 people
:
Probability (P) of selecting 2 men = 10/18 * 9/17 = 0.2941
P of selecting 5 women = 8/16 * 7/15 * 6/14 * 5/13 * 4/12 = 0.0128
P of two men and 5 women = 0.2941 * 0.0128 = 0.0038
:
P of selecting 3 women = 8/18 * 7/17 * 6/16 = 0.0686
P of selecting 4 men = 10/15 * 9/14 * 8/13 * 7/12 = 0.1538
P of 3 women and 4 men = 0.0686 * 0.1538 = 0.0106
:
P that the committee will be made of 2 men or 3 women = 0.0038 + 0.0106 = 0.0144 approximately 0.01
:
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