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

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

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

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

If the digits may not be repeated, there are 6x5x4x3x2x1 = 720 numbers, If digits can be repeated, the answer is 6x6x6x6x6x6 = 46,656 numbers If zero is ong the available digits but is excluded from the first place. 5x6x6x6x6x6=38,880 numbers

10

102

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.