2006 AMC 12B Problems/Problem 7
Problem
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?
Solution
First, we seat the children.
The first child can be seated in spaces.
The second child can be seated in spaces.
Now there are ways to seat the adults.
Alternative solution:
If there was no restriction, there would be 4!=24 ways to sit. However, only 2/4 of the people can sit in the driver's seat, so our answer is
See also
2006 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 6 |
Followed by Problem 8 |
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All AMC 12 Problems and Solutions |