SOLUTION: A committee of size 5 is to be selected at random from 3 women and 5 men. Find the probability that committee consists of: (1)all men. (2)all women.

(1)  First we find the numerator of the probability which is
the number of way to choose 5 men 

(5 men) CHOOSE (5 men) = 5C5 = 1 way

(That makes sense because we choose all the men in only 1 way.)

Now we find the denominator of the probability, which is the
number of ways to choose 5 people from the 8 people

(8 people) CHOOSE (5 people) = 8C5 = 56 ways

So the probability is 1 way out of 56 ways or 1/56.

(2)  First we find the numerator of the probability which is
the number of way to choose 5 women 

(3 women) CHOOSE (5 women) = 3C5 = 0

(That makes sense because you can't choose 5 women because 
there are only 3 women.)

So the probability is 0 ways out of 56 ways or 0/56 or 0.

(This cannot happen because there aren't enough women to choose 5)

Edwin