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Q: How many three digit numbers have no repeated digits?

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Using the digits of 1345678, there are 210 three digit numbers in which no digit is repeated.

It is possible to create a 3-digit number, without repeated digits so the probability is 1.

27 three digit numbers from the digits 3, 5, 7 including repetitions.

1

There are only two smaller 3-digit numbers and both of them have repeated digits.

48 of them if digits may not be repeated. 100 if they can.

The largest number with no repeated digits is 9,876,543,210 although it is 10 digits long, the largest 3 digit number with no repeated digits is 987

10

102

It is 99,887,765

If the digits may be repeated, there are four choices for the first digit, four choices for the second, and four choices for the third. Thus there are 4x4x4 = 64 possible three-digit numbers with those digits. If the digits may not be repeated, there are still four choices for the first digit, but then only three remaining choices for the second, and then just two choices for the third. In this case there are only 4x3x2 = 24 possibilities.

24+24+12+4=64.

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