# Pick Teams

From a group of 5 men and 7 women, in how many different ways can a team of 2 men and 3 women be formed?

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### 3 Responses to “Pick Teams”

1. Parth June 14, 2013 at 11:15 am #

So you multiplied 5 x 2 = 10 so did 7 and 3 get you 35?

2. Francini June 14, 2013 at 1:05 pm #

Can someone explain what 5/2 means? And 7/3 how are u getting 10 and 35?

3. Michael Corrao June 14, 2013 at 3:07 pm #

Extended explanation: If you got D. 4200, you interpreted this problem as a permutation, not as a combination. We do not care what order the men are picked in or what order the women are picked in, all we care is that there is a team of 2 men and a team of 3 women.

Permutation equation:

Combination equation:

Where n = total number of the group and r = the number of people we want. Hence,

n = 5 men
r = 2 men

We have 10 total possible combinations using the above formula.

The same goes for women.

n = 7 women
r = 3 women

We have 35 total possible combinations using the above formula.

Multiplied together, we have 350 possible combinations.