Hi guys,

I have a probability question:
A dance class consists of 22 students, of which 10 are women and 12 are men. If 5 men and 5 women are to be chosen and then paired off, how many results are possible?

I'm thinking first you find the combinations of 10 women while picking only 5. Also find the combinations of the 12 men choosing only 5 and then multiply those two combinations together. I don't know what I would do after this point though. Thanks for the help

Question

Hi guys,

I have a probability question:
A dance class consists of 22 students, of which 10 are women and 12 are men. If 5 men and 5 women are to be chosen and then paired off, how many results are possible?

I'm thinking first you find the combinations of 10 women while picking only 5. Also find the combinations of the 12 men choosing only 5 and then multiply those two combinations together. I don't know what I would do after this point though. Thanks for the help

compassionate · Answer

First I multiplied (10 nCr 5) times (12 nCr 5) to find how many groups of 10 people (with 5 women and 5 men) are possible. Then I think I multiply that number by 5! to account for the different male-female pairings that are possible. Is this right? Whoever gives the correct answer and detailed steps will get the best answer.

compassionate · Answer

^ Quoted from Answers.Yahoo

anonymous · Answer

the yahoo answers person is right
it's (10C5)*(12C5)*5!

anonymous · Answer

(10C5) is the number of women
(12C5) is the number of men
5! is the possible pairs

anonymous · Answer

thank you!

anonymous · Answer

np

anonymous · Answer

I gave the best response to compassionate since he answered a while ago. but thank you pizzapi for verification