For a 3 digit number, the left most or the most significant digit cannot be zero. So it can be 1,2,3,4,5,6,7,8 or 9 which is 9 possibilities. The middle number can be 0,1,2,3,4,5,6,7,8,9 which is 10 possibilties but one of the digits has been chosen already as the first digit, so the possibilities are only 9. The right most number can be 0,1,2,3,4,5,6,7,8,9 which is 10 possibilities but two of the digits have been already used by the left most and the middle digits. That leaves only 8 possibilities. So the total number of three digit numbers that have three distinct digits is
9 x 9 x 8 = 81 x 8 = 648 possibilities
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27 three digit numbers from the digits 3, 5, 7 including repetitions.
24 three digit numbers if repetition of digits is not allowed. 4P3 = 24.If repetition of digits is allowed then we have:For 3 repetitions, 4 three digit numbers.For 2 repetitions, 36 three digit numbers.So we have a total of 64 three digit numbers if repetition of digits is allowed.
It is possible to create a 3-digit number, without repeated digits so the probability is 1.
1,2,3,4 1+2+3+4=10 4 times 3 times 2 times 1 =24 24 counting numbers
Since both of those numbers contains four digits, there are no three-digit numbers between them.