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| Math Central | Quandaries & Queries |
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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.
Stephen.
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