Skip to main content

2006 AMC 12B Problem 7

Problem 7 of 25EasierCombinatorics

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?

Answer choices

Show solution

Solution

The driver is one of the two parents: 22 choices. Any of the remaining 33 people can sit in the front passenger seat, and the last 22 people fill the back in 22 orders. The total is 2⋅3⋅2=12.2 \cdot 3 \cdot 2 = 12. Thus, the correct answer is B.
AoPS wiki

Tagged: multiplication principle · arrangements with restrictions

More practice