Problem 11 · Counting the complement · 3 points
Made by AI and not reviewed by a real person.
A chameleon’s scarf has three patches numbered 1, 2, and 3. Each patch can be gold, teal, pink, or purple; how many different scarves have at least one gold patch?
- 36
- 64
- 48
- 37
- 27
Show a hint
- Count all possible scarves first.
- Subtract those with no gold patches.
Show the answer and solution
Answer: D — 37
Each of the three patches has 4 choices, giving 4 × 4 × 4 = 64 scarves. With no gold, each patch has 3 choices, giving 3 × 3 × 3 = 27 scarves. So the answer is 64 − 27 = 37. The tempting answer 48 comes from choosing which patch is gold and then coloring the other two, but it counts scarves with multiple gold patches more than once.