Problem 13 · 2015 Math Kangaroo
Medium
Counting & Probability
careful-counting
Joseph has got a toy car, a teddy bear, a ball and a ship. He wants to put them in a new order on the shelf. The ship must be next to the car, and the teddy bear should also be next to the car. In how many different orders can he put the toys on the shelf?
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Answer: B — 4
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Hint 1 of 2
The car must touch both the ship and the teddy, so the car sits between them.
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Hint 2 of 2
Treat ship-car-teddy as one block and place the ball at either end.
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Approach: form the forced block, then place the remaining toy
- The ship and the teddy both must be next to the car, so the car is in the middle of a block: ship–car–teddy.
- That block can be ordered 2 ways (ship–car–teddy or teddy–car–ship).
- The ball goes at the left end or the right end of the block: 2 choices.
- Total arrangements: 2 × 2 = 4.
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