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View Full Version : I want to know the answer!


d-nice
Sep 3, 2007, 09:17 AM
How many 4-digit combinations can you get from 0-9?

s_cianci
Sep 3, 2007, 09:33 AM
Is repetition of digits allowed or not? You didn't stipulate that. Also, is order relevant or not, e.g. should 1234 be considered the same as, say 4321? Your question states "combinations" which technically implies that order is not relevant so that has to be clarified as well. Either way, it boils down to: 1.) how many possibilities are there for the first digit? ; 2.) how many possibilities are there for the 2nd digit? ; likewise for digits 3 and 4. Then a quick multiplication does it. However, if order is not relevant, i.e. if 1234 counts the same as 4321 (since it's the same 4 digits, just in a different order), then you need to compensate. Ask yourself "how many times did I quadruple-count each combination" and divide your answer by that number.

galactus
Sep 3, 2007, 09:33 AM
That depends, is repetition allowed?

If repetition is allowed: 10^{4}

If not allowed: (10)(9)(8)(7)


See why?

d-nice
Sep 3, 2007, 09:40 AM
Repetition is allowed. 1234 as well as 4321 is allowed. And each # can be used more than once