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Six three-digit numbers contain only the digits 5 and 6. This is assuming you mean both the digits of 5 and 6. If not than 8, as it would include 555 and 666. 556, 565, 566, 655, 656, 665
There are 900 three-digit numbers.
Using the digits of 1345678, there are 210 three digit numbers in which no digit is repeated.
172
100-199 has 19 numbers200-299 has 100 numbers300-399 has 19 numbers400-499 has 19 numbers500-599 has 19 numbers600-699 has 19 numbers700-799 has 19 numbers800-899 has 19 numbers900-999 has 19 numbers(8x19)+100 = 152 + 100 = 252252 three digit numbers contain the digit 2