Uni Stuff > Mathematics

Number of Arrangements?

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kamil9876:
I have a solution but it involves some casework, so i will wait and see if there is a better one.

asa.hoshi:
haha.thanks for your help. but i kinda solved it. i used ur idea, _B_B_B_B_
and then placed the Rs and counted the possible ways to place the Gs w/o colour succession.
i.e. RB_B_B_BR, G must go where the _ and there is only 1 way to do it...
then i went on RBRB_B_B, x2 G must go where the _ are, and the remaining G can go in 5 different spots within the arrangement ect...
I came up with 79. I think its right.

kamil9876:
yeah that's the idea I used, I split it into four essentially different cases and the sum was 10 + 3*2*8 + 2*2*3 + 3*3=79.

It wouldn't be so nice for arbitrary number of bottles though, though maybe the problem is too complex for that.

asa.hoshi:
i think your way is more efficient.

hey at least we solved the problem  ;)

kamil9876:
if you wanna know the cases were:

X denotes where to place the remaining 5 bottles.

1) X B X B X B X B X

There are ways since u can just ignore the Bs to count.

2) B X X B X B X B X

If X X is G R then there are 3 ways (since the R can go in any remaining X). or if X X is R G then same story, so 2*3=6 ways. However this can be arranged in 8 differents ways like X X B X B X B X B etc. so 2*3*8 altogether.

3) B XX B XX B X B

4) B XXX B X B X B

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