Thread: Combination Problem

A lock is opened by pushing a series of buttons. Each of the three steps in the combination consists of either pushing one button or pushing two buttons simultaneously. A button may be used in more than one step. If there are 5 buttons then how many different combinations are there?

Originally Posted by fusion1455

A lock is opened by pushing a series of buttons. Each of the three steps in the combination consists of either pushing one button or pushing two buttons simultaneously. A button may be used in more than one step. If there are 5 buttons then how many different combinations are there?

At each step there are five ways to choose one button and there are ways to choose two buttoms.
So at each step how many can we choose?
Therefore since there are three steps, how many total?