2015 AMC 8 Problems/Problem 10
How many integers between and have four distinct digits?
The question can be rephrased to "How many four-digit positive integers have four distinct digits," since numbers between and are four-digit integers. There are choices for the first number, since it cannot be , choices for the second number, since it must differ from the first, choices for the third number, since it must differ from the first two, and choices for the fourth number, since it must differ from all three. This means there are numbers between and with four distinct digits.