2006 AMC 12B Problem 7

Below is the professionally curated solution for Problem 7 of the 2006 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2006 AMC 12B solutions, or check the answer key.

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Concepts:multiplication principle arrangements with restrictions

Difficulty rating: 1180

Mr. and Mrs. Lopez have two children. When they get into their family car, two people sit in the front, and the other two sit in the back. Either Mr. Lopez or Mrs. Lopez must sit in the driver's seat. How many seating arrangements are possible?

$4$

$12$

$16$

$24$

$48$

Solution:

The driver is one of the two parents: $2$ choices.

Any of the remaining $3$ people can sit in the front passenger seat, and the last $2$ people fill the back in $2$ orders.

The total is $2 \cdot 3 \cdot 2 = 12.$

Thus, the correct answer is B.

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