In how many different orders can five runners finish a race if no ties are allow

Ronin Daniels

Ronin Daniels

Answered question

2023-03-29

In how many different orders can five runners finish a race if no ties are allowed???

Answer & Explanation

Karma Gutierrez

Karma Gutierrez

Beginner2023-03-30Added 2 answers

To determine the number of different orders in which five runners can finish a race with no ties allowed, we can use the concept of permutations.
In a permutation, the order of arrangement matters. We want to find the number of permutations of the five runners.
The formula to calculate the number of permutations is given by:
P(n,r)=n!(nr)!
where n is the total number of objects (in this case, the number of runners) and r is the number of objects to be arranged (in this case, also the number of runners).
Let's calculate the number of permutations for this problem:
P(5,5)=5!(55)!
We have 5 runners (n = 5) and we want to arrange all of them (r = 5).
Simplifying the expression, we have:
P(5,5)=5!0!
The factorial of a number is the product of all positive integers less than or equal to that number. By definition, 0! is equal to 1.
Therefore, we can rewrite the expression as:
P(5,5)=5!1
Calculating the factorial:
5!=5×4×3×2×1=120
Substituting the values back into the expression, we have:
P(5,5)=1201=120
Therefore, the number of different orders in which five runners can finish the race with no ties allowed is 120.
So, P(5,5)=120.

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