# Thread: Groups of men and women

1. ## Groups of men and women

A group of 4 journalists is to be chosen to cover a murder trial. There are 5 male and 7 female journalists available. How many possible groups can be formed, consisting of 2 men and 2 women?

Here's what I have so far, I'd greatly appreciate any help

Men: 5 C 2 = 21
Women: 7 C 2 = 10

Would I then multiply these (21 x 10 = 210)?

2. Yes, you would multiply them. A slight correction:

$_7 C_2 = 21$
$_5 C_2 = 10$

3. Yay thanks so much I think I might be learning something!

4. Originally Posted by PiratePrincess
A group of 4 journalists is to be chosen to cover a murder trial. There are 5 male and 7 female journalists available. How many possible groups can be formed, consisting of 2 men and 2 women?

Here's what I have so far, I'd greatly appreciate any help

Men: 5 C 2 = 21
Women: 7 C 2 = 10

Would I then multiply these (21 x 10 = 210)?

Yes,

$\binom{5}{2}=10$ calculates the number of distinct groups of 2 men from the 5 available.

$\binom{7}{2}=21$ finds the number of groups of 2 women that can be selected from 7 women.

As any male group can be paired with any female group, the numbers of groups are multiplied.

M1W1 M1W2 M1W3......M1W21
M2W1 M2W2 M2W3.... M2W21
M3W1 M3W1 M3W3.... M3W21

all the way to the final pairings

M10W1 M10W2 M10W3......M10W21