2015 AMC 8 Problem 10

Below is the video solution and professionally curated solution for Problem 10 of the 2015 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2015 AMC 8 solutions, or check the answer key.

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Concepts:multiplication principle digits

Difficulty rating: 1070

10.

How many integers between $1000$ and $9999$ have four distinct digits?

$3024$

$4536$

$5040$

$6480$

$6561$

Video solution:

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Written solution:

First, there are $9$ digits to choose for the thousands digit since $0$ can't be chosen.

Then, after that, there are $9$ ways to choose the hundreds digit, $8$ ways to choose the tens digit, and $7$ ways to choose the ones digit. Therefore, we get $9\cdot9\cdot8\cdot7 = 4536$ ways to choose such an integer.

Thus, the correct answer is B .

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