SOLUTION: If a couple has six oys and six girls, how many gender sequences are possible?

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Question 654847: If a couple has six oys and six girls, how many gender sequences
are possible?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
it's:
12%21%2F6%216%21

=

=

=

=%28cross%282%29%2A11%2A2%2A3%2A2%2A7%29%2F%28cross%282%29%2A1%29

=11%2A2%2A3%2A2%2A7

=924

Here's why:
There are 12! unique ways the 12 children can be arranged.
Since we don't care about the order of the 6 boys, we divide by the number of ways 6 boys can be arranged, or 6!.
Similarly we don't care how the girls are arranged, so we divide again by 6!.
That leaves the number of ways 12 children consisting of 6boys and 6 girls can be arranged if you all you care about is gender.