How many even 3 digit numbers contain at least one 7. How many even 3 digit numbers contain at least one 7.
I got 126, but it was not an answer choice for the problem. Can anyone help?

Count the number of $3$ digit even numbers that do not contain $7$ and subtract from the total number of $3$ digit even numbers.

Let $xyz$ be the $3$ digit even number. Total number of $3$ digit even numbers is $450$, since $x$ has $9$ options, $y$ has $10$ options and $z$ has $5$ options. To obtain the number of $3$ digit even numbers that do not contain $7$, $x$ has $8$ options, while $y$ has $9$ options and $z$ continues to have $5$ options, i.e., $8 \times 9 \times 5 = 360$. Hence, the number of $3$ digit even numbers that contain at-least one $7$ is $450 - 360 = 90$.

