Problem:
An integer between and , inclusive, is chosen at random. What is the probability that it is an odd integer whose digits are all distinct?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
There are integers between and inclusive. For an integer to be odd it must end in , or . So there are choices for the units digit. For a number to be between and the thousands digit must be nonzero and so there are now choices for the thousands digit. For the hundreds digit there are choices and for the tens digit there are choices for a total number of choices. So the probability is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions