# Math Help - Combination Problem

1. ## 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?

2. 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 $\binom{5}{2}=10$ ways to choose two buttoms.
So at each step how many can we choose?
Therefore since there are three steps, how many total?