2002 AMC 8 Problem 19 — Solution | LIVE by Po-Shen Loh

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2002 AMC 8 Problem 19

Below is the professionally curated solution for Problem 19 of the 2002 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2002 AMC 8 solutions, or check the answer key.

All of the real AMC 8, AMC 10, AMC 12, and AIME problems in our complete solution collection are used with official legal permission of the Mathematical Association of America (MAA).

Concepts:digits casework

Difficulty rating: 1390

19.

How many whole numbers between $99$ and $999$ contain exactly one $0?$

$72$

$90$

$144$

$162$

$180$

Solution:

Note that the $0$ digit can either be the tens or the units digit. This gives us $2$ options for this.

There are $9$ options for each of the other digits for a total of $2 \cdot 9 \cdot 9 = 162$ numbers.

Thus, D is the correct answer.

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