How many ways are there to arrange 3 distinct books in a row?

How many ways are there to arrange 3 distinct books in a row?

• A. 3
• B. 9
• C. 12
• D. 6

Answer: (D)

Arranging in a row treats order as important, so we’re counting permutations of 3 distinct books. For the first position there are 3 choices, then 2 remaining choices for the second position, and 1 choice for the last position. Multiply: 3 × 2 × 1 = 6. So there are six possible orders: ABC, ACB, BAC, BCA, CAB, CBA. The other numbers don’t fit because they don’t account for using each book exactly once in all three positions (3 would ignore the rest, 9 would imply repeating or ignoring a position, etc.).

Arranging in a row treats order as important, so we’re counting permutations of 3 distinct books. For the first position there are 3 choices, then 2 remaining choices for the second position, and 1 choice for the last position. Multiply: 3 × 2 × 1 = 6. So there are six possible orders: ABC, ACB, BAC, BCA, CAB, CBA. The other numbers don’t fit because they don’t account for using each book exactly once in all three positions (3 would ignore the rest, 9 would imply repeating or ignoring a position, etc.).