Eleven people are competing in a sack race. There is a blue ribbon for first, a red ribbon for second, and white ribbon for third. How many different first-second-third place finishes are possible?
To find the number of different first-second-third place finishes in the sack race, we need to use the concept of permutations.
Permutations represent the number of ways to arrange a set of elements in a particular order. When order matters (as it does in this problem), we use permutations to count the number of possible arrangements. The formula for permutations is given by:
P(n, r) = n! / (n-r)!
Where n represents the total number of elements, and r represents the number of elements to be selected at a time.
In this case, we have eleven people competing for the three places (first, second, and third).
To find the number of different first-place finishes, there are 11 possibilities since any of the 11 people can come in first.
After someone comes in first, there are 10 people left who can take the second place. Thus, there are 10 possibilities for the second-place finish.
Finally, after the first and second places have been determined, there are 9 people remaining who can come in third place. Therefore, there are 9 possibilities for the third-place finish.
Using the permutation formula, we can calculate the total number of different first-second-third place finishes as follows:
P(11, 3) = 11! / (11-3)!
= 11! / 8!
= 11 × 10 × 9
= 990
Therefore, there are 990 different first-second-third place finishes possible in the sack race.
To determine the different first-second-third place finishes for the sack race, we can use the concept of permutations.
Since there are 11 people competing, there are 11 possible contenders for the first place. Once someone has taken first place, there are 10 remaining contenders for second place. Finally, after first and second places have been determined, there are 9 remaining contenders for third place.
To find the total number of possible finishes, we can multiply these three possibilities together:
Number of first place contenders = 11
Number of second place contenders = 10
Number of third place contenders = 9
Total number of different first-second-third place finishes = 11 x 10 x 9 = 990
Therefore, there are 990 different first-second-third place finishes possible in the sack race.