# 2017 AMC 8 Problems/Problem 20

Revision as of 14:07, 22 November 2017 by Nukelauncher (talk | contribs) (Created page with "==Problem 20== An integer between <math>1000</math> and <math>9999</math>, inclusive, is chosen at random. What is the probability that it is an odd integer whose digits are...")

## Problem 20

An integer between and , inclusive, is chosen at random. What is the probability that it is an odd integer whose digits are all distinct?

## Solution

There are options for the last digit, as the integer must be odd. The first digit now has options left (it can't be or the same as the last digit. The second digit also has options left (it can't be the same as the first or last digit). Finally, the third digit has options (it can't be the same as the three digits that are already chosen).

Since there are $9000 total integers, out answer is

~nukelauncher