Problem 21 · 2009 Math Kangaroo
Stretch
Counting & Probability
careful-countingcasework
In a vase there is one red, one blue, one yellow and one white flower. Maja the bee visits each flower exactly once. She begins with the red flower and she never flies directly from the yellow to the white flower. In how many different ways can she visit each flower?
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Answer: D — 4
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Hint 1 of 2
She always starts at the red flower, so list the orders of the other three.
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Hint 2 of 2
Then cross out any order where yellow comes immediately before white.
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Approach: list the routes and remove the forbidden ones
- Starting at red, the other three flowers (blue, yellow, white) can be ordered in 6 ways.
- Remove every order in which yellow is immediately followed by white.
- Two of the six orders are forbidden, leaving 4 allowed routes.
- So she can do it in 4 ways.
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