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Hi there so say there are 2 green hats (G) and 3 blue hats (B) and 3 are selected at random. How can I work out the number of different possible combinations? I.e.

BBB BBG BGG GBB GGB GBG BGB

I know the answers 7 having looked it up for this questions but was hoping someone might have a formula for working this out?

Thanks

N. F. Taussig
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    If you were picking 3 hats from an endless supply of green and blue hats, the formula would be $2\times 2\times 2=8$ (two choices per hat). The trick here is that GGG is impossible since there are only two green hats, so the actual answer is $8-1=7$. – Mike Earnest Sep 17 '17 at 22:15
  • The number of combinations can be found using the generating functions. The number of permutations of these combinations is a tougher task. – Jens Sep 19 '17 at 18:30

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