How many possible finish orders are there for 5 distinct horses?

How many possible finish orders are there for 5 distinct horses?

• A. 60
• B. 120
• C. 24
• D. 5

Answer: (B)

To count finish orders for five distinct horses, you’re arranging five different items in a line. The number of such arrangements is 5 factorial, which is 5 × 4 × 3 × 2 × 1 = 120. Think of it step by step: any of the five horses could win, then any of the remaining four could come in second, then three choices for third, two for fourth, and the last horse for fifth. Multiply to get 120 possible finish orders. The other numbers don’t fit because they reflect fewer distinguishable arrangements: 60 would be half of 120, as if two orders were treated the same; 24 is 4! from fixing one position or treating one horse as equivalent; 5 is just the count of horses, not the total orders.

To count finish orders for five distinct horses, you’re arranging five different items in a line. The number of such arrangements is 5 factorial, which is 5 × 4 × 3 × 2 × 1 = 120. Think of it step by step: any of the five horses could win, then any of the remaining four could come in second, then three choices for third, two for fourth, and the last horse for fifth. Multiply to get 120 possible finish orders. The other numbers don’t fit because they reflect fewer distinguishable arrangements: 60 would be half of 120, as if two orders were treated the same; 24 is 4! from fixing one position or treating one horse as equivalent; 5 is just the count of horses, not the total orders.