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Lining up my skittles



My pack of skittles comes in five flavors, grape, lemon, green apple, orange, and strawberry (odd that they don't have the cherry blue flavor found in the UK but alas).

Assume that my pack had the following proportion of flavors 2.5 lemon, 2 orange, 1.5 grape, 1.5 green, 1 strawberry. If i were to pour my skittles on the table and line them up in an offset two row pattern (so that at most, a single skittle touches four skittles [see image]. What are the chances that two skittles of the same color won't touch?


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Can you describe how you got that answer please?

I worked on it for a while until I decided it was just to complex for me to do without writing a program.

So, I generated all possible pairs of 9 & 8 long strings which together had 5 lemon, 4 orange, 3 grape,

3 green, and 2 strawberry colors. There are 17!/(5!*4!*3!*3!*2!) = 1,715,313,600 of these. Then, I

checked each one of them and counted those which had no same-color skittles touching. There were

1,232,600 like that. That gave me the probability I posted. The program was pretty sloppy but it

ran in 69 seconds on one core of my desktop machine.

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