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. (type an integer.)

Explanation:

Step1: Identify the problem type

This is a permutation problem where we need to find the number of ways 5 people can arrive, which is the number of permutations of 5 distinct objects.

Step2: Use the permutation formula

The number of permutations of \( n \) distinct objects is given by \( n! \) (n factorial), where \( n! = n\times(n - 1)\times(n - 2)\times\cdots\times1 \). Here, \( n = 5 \).

Step3: Calculate \( 5! \)

\( 5! = 5\times4\times3\times2\times1 = 120 \)

Answer:

120