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How many different 3 digit combinations can be made using numbers one through nine?
Through the magic of perms and coms the answer is 729
If using numbers 1 through 9 how many different 4 digit combinations can be made with no restrictions on order or repeats?
Each digit can appear in each of the 4 positions. There are 9 digits, therefore there are 9⁴ = 6561 such combinations.
If using numbers 0 through 9 how many different 2 digit combinations can be made?
If there are no restrictions on duplicated numbers or other patterns of numbers then there are 10 ways of selecting the first digit and also 10 ways of selecting the second digit. The number of combinations is therefore 10 x 10 = 100.
If using the numbers 1 through 9 how many different 3 digit combinations can be made?
If you allow digits to be repeated (for example, 222 or 992), then there are 9 x 9 x 9 = 729 combinations. If you do not allow digits to be repeated, then there are 9 x 8 x 7 = 504 combinations.
If using numbers 0 through 9 how many different 3 digit combinations can be made?
There are 10 possible digits that can be used: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. If you can only use each digit once, there are 10 choices for the first digit, 9 remaining choices for the second digit, and 8 remaining choices for the final digit - 10 x 9 x 8 = 720 combinations. If you can use each digit repeatedly, you have 10 choices for each digit - 10 x 10 x 10 = 1000 combinations.
