Kim, Maria, Ian, Jim, Sergio, 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 kim arrive first and simone last?

C. Find the probability that kim will arrive first and simone last.

Step-by-step explanation:

A. The order matters, so use permutations.  The number of ways that 6 people can be arranged is:

₆P₆ = 6! = 720

B. If Kim is first, and Simone is last, then the number of ways the remaining 4 people can be arranged is:

₄P₄ = 4! = 24

C. Of the 720 total arrangements, there are 24 in which Kim is first and Simone is last.  So the probability is 24/720 = 1/30.

b. hannah is playing with her cousin at