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There is no limitation given to the number of digits in the number, thus:

For 3 digit numbers: to be less than 500 the first digit can be only one of {1, 2, 3, 4} leading to 4 × 5 × 4 = 80 numbers

For 2 digit numbers: they are all less than 500, and there are 6 × 5 = 30 numbers

For 1 digit numbers: they are all less than 500, and there are 6 numbers

Thus there are in total 80 + 30 + 6 = 116 numbers that can be made form the digits {1, 2, 3, 4, 5 ,6} without repetitions that are less than 500.

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Q: How many numbers less than 500 can be formed using the digits 12345 and 6 without repetitions?
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