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

iohanetc

iohanetc

Answered question

2021-09-09

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

Answer & Explanation

aprovard

aprovard

Skilled2021-09-10Added 94 answers

Definition permutation (order is important):
P(n,r)=n!(nr)!
Definition combination (order is not important):
C(n,r)=(nr)=n!r!(nr)!
with n!=n(n1)21
Solution
We must apply the definition of permutation since the runners' order is crucial.
From the five runners, we'll pick five (as we want an ordering of all runners).
n=5
r=5
Consider the following when defining a combination:
P(5,5)=5!(55)!=5!0!=5120
Results: 120

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