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.