AMC 10 Weekly Practice Round 3

Complete problem set with solutions and individual problem pages

Problem 9 Medium

There are 5 cars to be parked in 6 adjacent parking spaces. Truck A is wider and occupies two spaces when parked, and car B cannot be parked next to truck A. How many different parking arrangements are there?

  • A.

    72

  • B.

    144

  • C.

    108

  • D.

    96

  • E.

    108

Answer:A

First, park truck A.

 

If truck A is not at the edge, there are 3 possible positions. In this case, car B has 2 possible positions. The other three cars (excluding A and B) can be arranged in _{3}P_{3} ways.

 

If truck A is at the edge, there are 2 possible positions. In this case, car B has 3 possible positions. The other three cars can also be arranged in _{3}P_{3} ways.

 

Therefore, the total number of parking arrangements is 3 \times 2 \times _{3}P_{3} + 2 \times 3 \times _{3}P_{3} = 36 + 36 = 72.

 

Thus, the answer is \text{A}.

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