SOLUTION: We have 20 women and 15 men. We want to form a delegation of 5 people. That delegation has to have 3 women. But Susy and Mary can't be together in the delegation.

We have a difficulty with the third sentence.
The statement "That delegation has to have 3 woman" can be taken
two ways.

1. that there must be EXACTLY 3 women and therefore EXACTLY 2 men. 
2. that there msut be AT LEAST 3 women, (i.e., there can be 3 women,
   4 women or all 5 women).

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I will assume it is the first way, that there must be EXACTLY 3 women 
and EXACTLY 2 men. If it's the second way, let me know in the thank-
you note form below, and I'll solve it that way.

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First we solve the problem without regard to whether Susy and Mary can 
be together or not.

Choose the 3 women 20C3 = 1140 ways
Choose the 2 men 15C2 = 105 ways.

That's (1140)(105) = 119700 ways.

Now from that number we must subtract the number of ways Susy and Mary
can be together.

Choose the other woman besides Susy and Mary in 20-2=18 ways.
Choose the 2 men 15C2 = 105 ways.

That's (18)(105) = 1890 ways.

So we subtract those 1890 forbidden ways from the 119700.

Answer 119700-1890 = 117810

Edwin