# 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 *committee arrangements* there are.

*Final answer:*

There are