2007 AMC 8 Problem 4

Below is the professionally curated solution for Problem 4 of the 2007 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2007 AMC 8 solutions, or check the answer key.

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Concepts:multiplication principle

Difficulty rating: 660

A haunted house has six windows. In how many ways can Georgie the Ghost enter the house by one window and leave by a different window?

$12$

$15$

$18$

$30$

$36$

Solution:

Georgie has $6$ options for which window he enters through. He, however, only has $5$ options for the exit since it must be different from the entrance.

The total number of paths is therefore $6 \cdot 5 = 30.$

Thus, D is the correct answer.

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