SOLUTION: you have 5 Gs and 9 Fs. How many ways can these letters be lined up if the Gs cannot be next to eachother?

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Question 915839: you have 5 Gs and 9 Fs. How many ways can these letters be lined up if the Gs cannot be next to eachother?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Treat each G as a "bar" (e.g. |) or divider and each F as a star. The problem is equivalent to finding number of ways to arrange 9 stars and 5 bars given that there is at least one stars separating any two bars, or the number of ways to put 9 indistinguishable balls into 5+1 = 6 distinguishable boxes, given that the middle four each contain at least one ball.

Put one ball into each of the middle four boxes, and now we are left with 5 balls and 6 boxes. The number of ways is (5+6-1)C5 = 10C5 = 252.