Library / UKMT Pink Kangaroo /215 of 220

UKMT Pink Kangaroo, 2025

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Five bricks are placed on the ground, as shown on the right. Navithan can only remove a brick if there are no bricks on top of it. He repeatedly removes a brick, chosen at random from those available, until all the bricks are removed. What is the probability that the brick numbered 4 is the third one to be removed?

(A) $\frac{1}{3}$ (B) $\frac{1}{4}$ (C) $\frac{1}{5}$ (D) $\frac{1}{6}$ (E) $\frac{1}{8}$

Figure for this problem

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.