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I'm trying to find the average result for a game where you have 12 items (containing a score), you can pick up to five of them, one of them is a multiplier, that when selected multiplies your result by it ( for example a x2).

How do I have to approach this problem? Do I have to analyze case by case, first by setting all the 11 numbers and the multiplier, and then making the calculus, or can I find a generic formula where I insert this values and find my expected result.

The expected result of the game, is calculated with the sum of the 5 itemes selected, with the exception where the multiplier is selected, where the sum of the other 4 is multiplied by it.

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up vote 6 down vote accepted

You can do it generically. Treat the case of the multiplier separately. So there's 11C5 (eleven choose 5) ways with no multiplier. You want the average. It's just 5 times the average of those eleven numbers. Then there's 11C4 ways with the multiplier. Let the multiplier be k. The average for the other 4 will be 4 times the average of the eleven. So, if A's the average, you have 4Ak.

So, ((11C5)*5A + (11C4)*4Ak)/(12C5) is your answer :)

Then simplify.

I get (35+20k)A/12. Hope that's right.

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I will try this out, and then let you know about it. – miguel.hpsgaming Jul 4 '11 at 13:32
Works great! Thank you. – miguel.hpsgaming Jul 4 '11 at 15:16
Awesome, it was a fun problem :) – user826788 Jul 4 '11 at 15:26
The extended formula version should be:((11C5)*5A + (11C4)*4Ak)/(12C5) The first term was missing the 5 multipling the average of the eleven numbers! – miguel.hpsgaming Jul 4 '11 at 18:02
Doh! Fixed now :) – user826788 Jul 5 '11 at 3:31

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