Question

The registration numbers of vehicles in a certain country use digits 1-999. If a visitor has just entered the country. What is the probability that the first car he sees has at least 2 identical digits?

Ans: 29/111

Answer 1

Assuming leading zeroes count as digits, then probability of seeing 3 distinct digits
= 10*9*8/1000
= 720/1000
=18/25
Probability of at least 2 identical digits
= 280/1000
=7/25

If leading zeroes are not displayed, then
there are 9*9*8=648 plates with distinct digits between 100-999
and 90 between 1 and 99
for a total of 738 out of 999 plates.
So probability of plates with at least 2 identical digits is
(999-738)/999
=29/11

Answer 2

Last line should read
29/111

Answer 3

How do you get 738/999??