2007 AMC 8 Problem 4

Attempt Problem 4 of the 2007 AMC 8 below, then check your answer against the professionally curated solution 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.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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?

$12$

$15$

$18$

$30$

$36$

Answer: D

Concepts:multiplication principle

Difficulty rating: 660

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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