Question

tyrone, kim, sarah, eduardo, and simone have all been invited to a dinner party. they arrive randomly and each person arrives at a different time.
a. in how many ways can they arrive?
b. in how many ways can tyrone arrive first and simone last?
c. find the probability that tyrone will arrive first and simone last.
a. 120 (type an integer.)
b. \square (type an integer.)

Explanation:

Step1: Identify fixed positions

Tyrone is first, Simone is last. So we fix these two positions.

Step2: Arrange remaining people

We have 3 remaining people (Kim, Sarah, Eduardo) to arrange in the middle 3 positions. The number of permutations of 3 people is \(3!\).
\(3! = 3\times2\times1 = 6\)

Answer:

6