a committee of 3 is to be formed from a group consisting of 5 men and 2 ladies.
find the probability that(1) the committee does not include any lady
That's the probability of selecting 3 men from the 5.
The number of ways to select 3 men is
5 men Choose 3 or 5C3 or C(5,3) = 10 ways
The number of ways to select ANY 3 from the 7 humans is
7 humans Choose 3 or 7C3 or C(7,3) = 35 ways
That's 10 ways out 35 ways or 
which reduces to 
.
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(2)the committee includes both the ladies.
We only need to choose 1 of the 5 men to go with the two ladies.
That's 5 ways out of 35 ways or 
which reduces to 
.
Edwin
