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.

-

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.