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There are 900 possible combinations, starting with 1005....

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If the digits can't repeat . . .

The first can be 1, 2, 3, 4, 6, 7, 8, or 9 . . . 8 choices. For each one . . .

The second can't be 5 or the one used . . . 8 choices. For each one . . .

The third can't be 5 or the two used . . . . . 7 choices. For each one . . .

The fourth one is 5.

Total number of possibilities = (8 x 8 x 7 x 1) = 448.

If the digits can repeat:

The first can be any one of 9 choices (all except zero). For each one . . .

The second can be any of 10 choices. For each one . . .

The third can be any one of 10 choices. For each one . . .

The fourth is 5.

Total number of possibilities = (9 x 10 x 10 x 1) = 900.

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Q: How many 4 digit combinations can be made using 0 through 9 and using each number only once?
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