Math CentralQuandaries & Queries


Question from Jeffrey:

Hi, I was having a disagreement with a friend as to the answer to this question.  We have a 5 button push lock and we were wondering how many different codes were possible in this situation.  In this lock each button can only be pressed once (ie it's not a numbered key pad) and order matters.  How would we find out the # of possible codes?

Hi Jeffrey.

I infer from your description that you have 5 buttons and all of them must be pushed once each, but that the order matters. If I'm wrong, let me know in what way.

Think about it this way:

  • There are five choices for the first button you push.
  • There are four choices left for the second button.
  • There are three choices left for the third.
  • Two choices are left for the second.
  • And the last button is the only one remaining.

We call this a "permutation" question. The way to solve it is to multiply the number of choices together:
      5×4×3×2×1 = 120.

There are 120 possible codes.


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