Math CentralQuandaries & Queries


Question from Rourke:

how many possible combinations are there in a 4 digit lock with 6 numbers which can repeat themselves.


It seems you have a lock with 4 dials and each dial can have any one of six digits, maybe 1, 2, 3, 4, 5 and 6. You want to know how many different combinations are possible.

Start with the leftmost dial. There are 6 possibilities for this dial. Once you have chosen one look at the next dial. Regardless of what you chose for the first dial there are 6 possibilities for the second. Thus for the first two dials there are $6 \times 6$ possible choices. Once you have chosen one of these, how many possibilities are there for the third dial? How many possibilities choices are there for the first three dials?

I hope this helps,


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