Question

Ian, jim, sergio, dawn, katrina, eduardo, sarah, 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 katrina arrive first and tyrone last

Answer 1

There are 720 ways in which Katrina can arrive first and Tyrone last to a dinner party, calculated by finding the factorial of the number of people arriving between them, which is 6 factorial or 720.

Step-by-step explanation:

The question asks to calculate the number of ways Katrina can arrive first and Tyrone last to a dinner party with a total of 8 invitees, which is a permutation problem. We assume Tyrone is an additional person to the list as his name was not mentioned in the initial list of invitees. Since the order of arrival matters and there are 6 people between Katrina and Tyrone, we are interested in the different ways those 6 can arrive.

This leaves 6 spots to be filled by 6 people (Ian, Jim, Sergio, Dawn, Eduardo, and Sarah), and each of these spots can be filled in any order. The number of permutations is therefore the factorial of the number of individuals, which is 6 factorial or 6!.

The calculation is then: 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720.

So, there are 720 ways in which Katrina can arrive first and Tyrone last while the remaining guests arrive in any order.