A traffic light features 5 colors: Red, Blue, Green, Yellow, and Orange. If signals are created by selecting any $3$ of these $5$ colors, how many distinct signals can the traffic light display if the sequence of colors matters?

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120

240

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Official Explanation

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To determine the number of unique signals, we first select 3 colors from the 5 available colors: Red, Blue, Green, Yellow, and Orange. The number of ways to choose 3 colors from 5 is given by…

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Comments

DharunAug 27, 2024

this pattern comes up frequently

sawaiFeb 17, 2024

Thank for sharing!

What this question tests

What it tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Common trap

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.

A traffic light features 5 colors: Red, Blue, Green, Yellow, and Orange. If signals are created by selecting any 333 of these 555 colors, how many distinct signals can the traffic light display if the sequence of colors matters?