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Math Help - Combination Problem

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    Question 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?
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    Quote Originally Posted by fusion1455 View Post
    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?
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