Math CentralQuandaries & Queries


Question from Markbo:

A combination lock has 0-9 plus Y on its keypad. A code is generated by selecting 4 digits from those keys (0-9 and Y) with no repeated choices, but sequence does not matter
(i.e. 1-2-3-4 is the same as 4-3-2-1, and the same as 3-4-1-2 and counts as one combination)

How many different 4-digit codes are possible in this scenario?



From your description you have a 3 digit code and a mandatory Y. The number of 3 digit codes is the number of ways of choosing 3 thing from 10 things, the ten things being 0-9. Mathematicians call these combinations so you want the number of combinations of 10 things taken 3 at a time, or sometimes "10 choose 3".

To calculate this I suggest you look at our response to an earlier question.


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