Thread: probability

the registration numbers of vehicles in certain country use digits 1 to 999. if a visitor has just entered the country, wht is the probbability tht the first car he sees has at least 2 identical digits. answer provided is (29/111). show me the soloution please

Hello, qweiop90!

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

There are 999 possible numbers.

The opposite of "at least two identical digits" is "no matching 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 with no matching digits.

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


Therefore: .