How many ways can you arrange four distinct items?

How many ways can you arrange four distinct items?

• A. 12
• B. 24
• C. 6
• D. 4

Answer: (B)

When order matters, count by multiplying the choices for each position. For four distinct items, you have 4 options for the first spot, then 3 for the second, 2 for the third, and 1 for the last. Multiply: 4 × 3 × 2 × 1 = 24. This is 4! (four factorial), so there are 24 possible arrangements. The other numbers come from counting fewer positions: 12 would be the count if you were arranging only two items, 6 would be the count for three items (3!), and 4 would be choosing a single item or looking at non-ordered selections.

When order matters, count by multiplying the choices for each position. For four distinct items, you have 4 options for the first spot, then 3 for the second, 2 for the third, and 1 for the last. Multiply: 4 × 3 × 2 × 1 = 24. This is 4! (four factorial), so there are 24 possible arrangements.

The other numbers come from counting fewer positions: 12 would be the count if you were arranging only two items, 6 would be the count for three items (3!), and 4 would be choosing a single item or looking at non-ordered selections.