# Average result of game

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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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