Wednesday, August 06, 2008

Well Waddaya Know XX

Last week's Q & A:
I have 10 marbles - 5 red, 2 green, and 3 blue. How many different ways can I line them up?
2,520
10 (37%)
3,628,800
9 (33%)
120,960
5 (18%)
4,032
3 (11%)


Votes so far: 27
Ezzie: For what it's worth, while I knew what had to be done, I could not remember how to figure it out; I still realized it had to be 2,520 (the other numbers were too high), but it was very tricky.

Shragi:
10!
_____ =
5!*3!*2! 2520
10! = arrangement of 10 marbles
since switching around 2 (for example) red marbles gives the same
arrangement twice we remove all the possibilities which repeat
themselves.
Therefore we divide by 5! (=possibilities to arrange the reds)
3! (= possibilities to arrange the blues)
2! (= possibilities to arrange the greens)

This week's question is up to the left.

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