2023 CEMC Fermat Problems/Problem 6

Problem

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?

$\text{ (A) }\ 8 \qquad\text{ (B) }\ 7 \qquad\text{ (C) }\ 5 \qquad\text{ (D) }\ 4 \qquad\text{ (E) }\ 3$

Solution

Each door has $2$ possibilities for the color and there are $3$ doors, so there are $2^3$ ways to paint the doors.

This gives $\boxed {\textbf {(A) } 8}$ ways.

~anabel.disher

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2023 CEMC Fermat Problems/Problem 6

Problem

Solution