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Question

You are one of 10 students performing in a school talent show. The order of the performances is determined at random. The first 5 performances go on the stage before the intermission. a. What is the probability that you are the last performer before the intermission and your rival performs immediately before you. b. What is the probability that you are not the first performer.

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 3a) If we fix ourselves on the 5th place, and our rival on the 4th, there are eight other performers who can be arranged $8!$ different ways. The total number of ways all performers can be arranged is $10!$ so to get the probability, we need to divide the satisfactory events by the total number of events:

$\dfrac{8!}{10!}=\dfrac{1}{90}$

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