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Number Theory/Factorial question.


I am trying to figure out the equation for this situation. It is a modified factorial. You have 5 buttons. Each button can be pressed individually or in combination with other buttons. Your button press sequences can range from 1 individual or combination button press to five individual or combination button presses so long as any one button is pressed only one time.  How many different combinations can you generate?

Hello bart
You have used the word combination, which means you are not interested in the order that the buttons are pressed.  Only in the final result.  In this case each button can be pressed or not pressed.  2 possibilities for each, so that makes 2^5 = 32 ways.  But I think my understanding is that you must have at least one button pressed, making 31 ways.
If instead you want the number of permutations, so the order of pressing is important, there would be 5 ways for 1 button, 5*4 ways for 2 buttons, 5*4*3 ways for 3, 5*4*3*2 for 4 and 5*4*3*2*1 for 5.  That makes 325.

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