How many permutations of 3 distinct items exist?

Study for the Logical Reasoning STEM Test. Practice with flashcards and multiple-choice questions, each with hints and explanations. Prepare for success!

Multiple Choice

How many permutations of 3 distinct items exist?

The idea being tested is that when order matters, you count permutations by multiplying the number of choices available at each step. For three distinct items, there are 3 choices for the first position, 2 remaining choices for the second, and 1 choice for the last. Multiply them: 3 × 2 × 1 = 6. This is 3!, the number of ways to arrange three distinct items. So there are six possible permutations. The other numbers don’t fit because they don’t reflect the decreasing number of available options as each position is filled, or assume repetition where the items must be distinct.

The idea being tested is that when order matters, you count permutations by multiplying the number of choices available at each step. For three distinct items, there are 3 choices for the first position, 2 remaining choices for the second, and 1 choice for the last. Multiply them: 3 × 2 × 1 = 6. This is 3!, the number of ways to arrange three distinct items.

So there are six possible permutations.

The other numbers don’t fit because they don’t reflect the decreasing number of available options as each position is filled, or assume repetition where the items must be distinct.

More practice questions