2003 AMC 8 Problems/Problem 16

Problem

Ali, Bonnie, Carlo, and Dianna are going to drive together to a nearby theme park. The car they are using has $4$ seats: $1$ Driver seat, $1$ front passenger seat, and $2$ back passenger seat. Bonnie and Carlo are the only ones who know how to drive the car. How many possible seating arrangements are there?

$\textbf{(A)}\ 2\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 6\qquad\textbf{(D)}\ 12\qquad\textbf{(E)}\ 24$

Solution

There are only $2$ people who can go in the driver's seat--Bonnie and Carlo. Any of the $3$ remaining people can go in the front passenger seat. There are $2$ people who can go in the first back passenger seat, and the remaining person must go in the last seat. Thus, there are $2\cdot3\cdot2$ or $12$ ways. The answer is then $\boxed{\textbf{(D)}\ 12}$ .

Solution 2 (Quick)

If there weren't any extra requirements, there would be 24 combinations. However, there are only 2, which is half of 4, ways to put the people for the first seat by restriction. Therefore, half of 24 is $\boxed{\textbf{(D)}\ 12}$ .

Solution by ILoveMath31415926535

Video Solution

2003 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 15	Followed by Problem 17
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2003 AMC 8 Problems/Problem 16

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Problem

Solution

Solution 2 (Quick)

Video Solution

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