SOLUTION: how many ways can a jury of 4 men and 4 women be selected from twelve men and ten women?

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Question 235778: how many ways can a jury of 4 men and 4 women be selected from twelve men and ten women?
Found 2 solutions by josmiceli, nyc_function:
Answer by josmiceli(6784) About Me  (Show Source):
You can put this solution on YOUR website!
12%2A11%2A10%2A9+=+11880 ways to choose 4 men from 12 men
10%2A9%2A8%2A7+=+5040 ways to choose 4 women from 10 women
Each of the 11880 groups of 4 men can combine
with each of the 5040 groups of 4 women in
11880%2A5040+=+59875200 ways

Answer by nyc_function(2643) About Me  (Show Source):
You can put this solution on YOUR website!
12P4 + 10P4 =
The number of permutations of n objects taken r at a time is:
nPr = n!/(n - r)!
We each separately and then add the results.
12P4 = 12!/(12 - 4)!
12P4 = 479001600/8!
12P4 = 479001600/40320
12P4 = 11,880
=============================================
10P4 = 10!/(10 - 4)!
10P4 = 3628800/6!
10P4 = 3628800/720
10P4 = 5040
=============================================
We now add both.
12P4 + 10P4 = 11,880 + 5040
12P4 + 10P4 = 16,920 ways