Hello, qweiop90!

There are 999 possible numbers.The registration numbers of vehicles in certain country use digits 1 to 999.

If a visitor has just entered the country, what is the probbability that

the first car he sees has at least 2 identical digits?

Answer: 29/111

The opposite of "at least two identical digits" is "nomatching digits."

. . How many numbers have no matching digits?

There are: . one-digit numbers.

For two-digit numbers:

The first digit is not zero . . . there are 9 choices.

The second digit can be any digit except the first digit: 9 choices.

. . There are: . two-digit numbers.

For three-digit numbers:

The first digit is not zero . . . there are 9 choices.

The second digit can be any digit except the first digit: 9 choices.

The second digit can be any of the remaining 8 digits: 8 choices.

. . There are: . three-digit numgers.

So there are: . numbers withnomatching digits.

Hence, there are: . numbers with some matching digits.

Therefore: .