🦘 Math Kangaroo Grade All Felix 1-2 Ecolier 3-4 Benjamin 5-6 Kadett 7-8 Junior 9-10 Student 11-12 ⇄ switch contest
2009 Math Kangaroo

Problem 21

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?

Show answer
Answer: D — 4
Show hints
Hint 1 of 2
She always starts at the red flower, so list the orders of the other three.
Still stuck? Show hint 2 →
Hint 2 of 2
Then cross out any order where yellow comes immediately before white.
Show solution
Approach: list the routes and remove the forbidden ones
  1. Starting at red, the other three flowers (blue, yellow, white) can be ordered in 6 ways.
  2. Remove every order in which yellow is immediately followed by white.
  3. Two of the six orders are forbidden, leaving 4 allowed routes.
  4. So she can do it in 4 ways.
Mark: · log in to save