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Revision as of 14:07, 17 November 2022
Problem
How many three-digit positive integers have an odd number of even digits?
Solution
There are only 
ways for an odd number of even digits: 
even digit or all even digits.
Case 1: even digit
There are 
ways to choose the odd digits, 
ways for the even digit, and 
ways to order the even digit. So, 
. However, there are 
ways that the hundred's digit is 
and we must subtract this from 
, leaving us with 
ways.
Case 2: all even digits
There are 
ways to choose the even digits, and ways where the hundred's digit is . So, 
.
Adding up the cases, the answer is 
.
~MrThinker
See Also
| 2022 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
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