Question

How many three-digit positive integers have an odd number of even digits?

$150$

$250$

$350$

$450$

$550$

Solution:

First, we can choose any combination for the first two digits. This would have $9\cdot 10 = 90$ choices.

Then, if there are an odd number of even digits among them, I make the units digit odd, which can be done in $5$ ways. Otherwise, I make the units digit even, which can be done in $5$ ways. Regardless of my choice of the first two digits, I have $5$ ways to choose the units digit.

Therefore, there are $90$ ways to choose the first two digits, and $5$ ways to choose the last digit, so the total number of ways is $90\cdot 5 = 450.$

Thus, the answer is D .

2022 AMC 10B Problem 3

Solution:

Problem 3 in Other Years