Question 16

There are 720 possible finishing orders in a horse race with 6 horses.

The number of possible finishing orders can be determined by calculating the factorial of the number of horses, which is 6!. This results in 6 x 5 x 4 x 3 x 2 x 1 = 720.

A) 120

This option represents the factorial of 5 (5!), which only accounts for the finishing orders of 5 horses, not 6. Therefore, this answer is incorrect as it does not consider all horses in the race.

B) 240

This option suggests a calculation of 4! x 6, which does not represent the correct factorial calculation for 6 horses. Thus, it is also incorrect as it underestimates the total number of finishing orders.

C) 360

This option represents 6! divided by 2, which is an incorrect method of calculating the total number of finishing orders. The correct approach involves using the full factorial of 6 without any divisions, making this choice incorrect.

D) 720

This option is correct as it accurately represents 6!, which calculates the total number of unique finishing orders for 6 horses. The factorial of 6 is 720, confirming this option as the correct answer.

Conclusion

The correct answer of 720 is derived from calculating 6! for six horses, showcasing the total distinct finishing orders possible. All other options fall short in their calculations or misinterpret the factorial concept, making them incorrect in the context of the problem.