Isn't the combination of 3 one gender and 1 the other gender 4C1*3C3? However that only takes into account ONE gender combo.
I agree with that.Couple are planning four kids. What is more likely: both genders equal (2 boys, 2 girls) or 3 of one gender and 1 of the other gender?
But is really ? I'd say it is rather .
How could they get in the numerator?!
Is there already any [tex] keyboard shortcut? I vote for FN/CTRL+M.
In this one, there ARE only 16. Enumerate them.
4 vs 0
BBBB
GGGG
3 vs 1
BBBG
BBGB
BGBB
GGBG
GGGB
BGGG
GBBB
GBGG
2 vs 2
GBBG
GBGB
GGBB
BGBG
BGGB
BBGG
Of course, had you pondered one important thing, you would have kept trying. After counting 2 vs 2, you could have counted 4 vs 0 and subtracted, since there are only three types. This would have discouraged your result.
Further, a little binomial expansion would reveal it.
It's pretty obvious from that.
The REAL lesson is that there are many ways to proceed. If you know only one way, you will not have a backup plan or an alternative approach.