Permutations and Combinations

Hi Guys, I have a question on Permutations and Combinations. I have come across this question and it reads:

"In how many ways can a committee of five men and four ladies be selected from a group of eight men and six ladies"

I think this is a combinations question and I would appreciate it if i could get some help with answering it. I have included a template as how i want the answer to be answered and i would appreciate if the answer could be provided using it.

n C r = n!
------------ =
n!(n-r)!

( Sorry that the formula above is displayed this way, but the editor wont allow me to display it the way that i want, im sure the people who know about this topic will understand the formula)

Can you please tell me step by step how you got the answer as i really would like to understand how to answer this question. Many Thanks.

First, the actual equation is n C r = n!
-----------
r!(n-r)!
Now to answer your question:
You are half right. This is actually two combination equations. first, find the number of combinations of men, then of women, and multiply.
r=5 n=8
8!
---------
5!(8-5)!

40320
----------
720

56 combinations of men.
Now the women.

n =6 r =4

6!
--------------
4!(6-4)!

720
-----------
48

15 combinations of women.
Now we multiply the men (56) by the women (15) to get the total possible combinations: 840

I'm not doing it the way you want because I'm not familiar with it, and because it requires more typing than is necessary.

Five men from 8 so 8C5
four ladies from 6 so 6C4

Five men and 4 ladies = 8C5 x 6C4

Apparently 840 is the answer

So n is the front number, r is the latter. Input that into your formula and bang, also I think someone pointed out you got the formula wrong. Why on earth use it though when scientific calculators will do it for you!

8C5 * 6C4 - 840

The events are mutually exclusive therefore we multiply them