There are eight sprinters competing for first, second, and third place ribbons. How many different ways can the ribbons be awarded?
To determine the number of different ways the ribbons can be awarded to the sprinters, we can use the concept of permutations.
For the first place ribbon, any one of the eight sprinters can win, so there are 8 possibilities for the first place.
After the first place winner is determined, there are seven remaining sprinters who can win the second place ribbon. Therefore, there are 7 possibilities for the second place.
Once the first and second place winners are determined, there are six remaining sprinters who can win the third place ribbon. Hence, there are 6 possibilities for the third place.
To find the total number of different ways the ribbons can be awarded, we multiply the number of possibilities for each place:
8 possibilities for the first place × 7 possibilities for the second place × 6 possibilities for the third place = 336 different ways the ribbons can be awarded.
To find the number of different ways the ribbons can be awarded, we can use the concept of permutations.
In this problem, we have 8 sprinters competing for the ribbons.
To find the number of ways the ribbons can be awarded, we need to calculate the number of permutations of 8 objects taken 3 at a time.
The formula to calculate permutations is given by:
P(n, r) = n! / (n-r)!
Here, n represents the total number of objects (sprinters) and r represents the number of objects taken at a time (ribbons awarded).
Using the formula, we can calculate the number of permutations:
P(8, 3) = 8! / (8-3)! = 8! / 5!
Calculating:
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320
5! = 5 * 4 * 3 * 2 * 1 = 120
Substituting the values:
P(8, 3) = 40,320 / 120 = 336
Therefore, there are 336 different ways the ribbons can be awarded.