6 runners run in a 500 yard dash. Prizes are awarded for 1st, 2nd, and 3rd place. Assume there are no ties, how many different orders can the runners finish 1st, 2nd, and 3rd?
P(6,3) = 6*5*4
120
To determine the number of different orders the runners can finish in 1st, 2nd, and 3rd place, we can use the concept of permutations.
In this scenario, we have 6 runners competing for the top 3 positions. To find the number of different orders they can finish, we need to calculate the number of permutations of the 6 runners taken 3 at a time.
The formula for permutations is:
P(n, r) = n! / (n - r)!
where n is the total number of objects and r is the number of objects taken at a time.
In this case, n = 6 (number of runners) and r = 3 (number of positions to be filled).
Using the formula, we can calculate the number of different orders:
P(6, 3) = 6! / (6 - 3)!
= 6! / 3!
= (6 x 5 x 4 x 3 x 2 x 1) / (3 x 2 x 1)
= 6 x 5 x 4
= 120
Therefore, there are 120 different orders the runners can finish in 1st, 2nd, and 3rd place.