Problem 9 · 2023 Math Kangaroo
Easy
Counting & Probability
careful-counting
Anna has five circular discs that are all of different sizes. She wants to build a tower using three discs, where a smaller disc always has to lie on top of a bigger disc. How many ways are there for Anna to build the tower?
Show answer
Answer: D — 10
Show hints
Hint 1 of 2
Once three discs are chosen, how many valid stacking orders are there?
Still stuck? Show hint 2 →
Hint 2 of 2
Since sizes are all different, the order is forced, so just count the choices of three discs.
Show solution
Approach: count the ways to choose three discs (order is forced)
- For any three chosen discs, the smaller-on-bigger rule fixes exactly one stacking order.
- So the number of towers equals the number of ways to choose 3 discs from 5.
- That is C(5,3) = 10.
- So the answer is 10 (D).
Mark:
· log in to save