How many committee of size 5 consisting of 3 men and 2 women can be seated from 8 men and 6 women if a certain man must not be on the committee ?
1 Answer
There are
Explanation:
In the problem you have
Since one man is not allowed to be in the committee, we can take out one man from the list (it doesn't matter; for simplicity's sake, I will take out Man 8)
Then we need to find out how many arrangements of men and arrangements of women, then multiply them.
Arrangements of Men
Since the order in which the men are chosen does not matter, and you cannot choose the same man twice, we can use combinations.
The formula is
If we are choosing
So there are
Arrangements of Women
We can do the same process for women: using combinations.
The formula is
If we are choosing
So there are
Counting Principle
Now we know that there are
Final answer:
There are