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Problem 162

Combinatorics Difficulty 1.2 Multiple choice CEMC Fermat · Canada · 2023

Vivek is painting three doors. The doors are numbered 1, 2 and 3.
Each door is to be painted one colour: either black or gold. One
possibility is that door 1 is painted black, door 2 is painted gold, and
door 3 is painted gold. In total, how many different ways can the three
doors be painted?

Pick one

Official solution

Since there are 3 doors and 2 colour choices for each door, there
are $2^3 = 8$ ways of painting the
three doors.

Using “B” to represent black and “G” to represent gold, these ways are
BBB, BBG, BGB, BGG, GBB, GBG, GGB, and GGG.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.