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?
The Attempt at a Solution
We can say that for the first couple, there are a pool of 12 possible men to choose from and a pool of 10 possible women to choose from. So there are 12x10=120 possible couples. For the second couple, there are a pool of 11 men and a pool of 9 women. So 9x11=99. and so on until we get to the fifth couple (8x6=48). Then we add all the numbers together (120+99+80+63+48=410 possible 5 couple combinations). Is this the correct reasoning? I feel I'm missing something here.