Problem 20 · 2012 Math Kangaroo
Stretch
Counting & Probability
careful-countingcasework
Anna, Laura, Lisa and Katharina wanted to take a photo together. Anna and Katharina are best friends and wanted to stand next to each other. Lisa also wanted to stand next to Anna. In how many different ways can the photo be taken, if all their wishes are met?
Show answer
Answer: B — 4
Show hints
Hint 1 of 2
Anna must stand next to both Katharina and Lisa, so Anna is in the middle of those two.
Still stuck? Show hint 2 →
Hint 2 of 2
Treat Katharina-Anna-Lisa as one block and place Laura at either end.
Show solution
Approach: bundle the friends who must be adjacent
- Anna is next to Katharina and next to Lisa, so the order around Anna is Katharina-Anna-Lisa (or its reverse): 2 ways.
- This block of three can have Laura at the left end or the right end: 2 ways.
- That gives 2 x 2 = 4 line-ups.
- There are 4 ways.
Mark:
· log in to save