Math CentralQuandaries & Queries


Question from Michael:

We have a 3 digit lock that only allows for 5 possible numbers to be used. (The numbers can repeat) What are the total number of combinations that can be created.

Hi Michael,

Think about randomly guessing the combination. For the first digit you have 5 choices and regardless of your choice you have 5 choices for the second digit. Thus you have 5 × 5 = 55 = 25 choices for the first two digits.

Finally, whatever choices you have made for the first two digits you have 5 choices for the third digit. Thus in total you have 5 × 5 × 5 = 53 = 125 possible combinations.


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