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I stumbled across a question in mathematics which left me confused.

Apparently there is a character in a computer game that has 10 different actions.

Which action he makes is determined by which combination of buttons that you press. You should press three buttons and gets to choose between W, Q, and P. The order of the buttons are irrelevant, i.e. WQP is identical to QWP, etc. Then also be repeated, i.e. you can press WWQ.

When I write down the combos, I find the 10 different ones.

But when I try to calculate the result, I get confused.

My first guess was to calculate 3^3 / 3!, but this doesn't even give me an integer!

Sorry for my english.

Please help.

/Kontilera

ps. This is not a homework, only friend to friend conversation that left me curious. ds.

pss. I realized the answer must be 5 nCr 3. But is there any way to get an intuition for why? dss.

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# Combinatorics from Warcraft

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