Question

A bookstore is organizing a panel discussion for an event. There are 8 authors, and the organizers need to choose a moderator, a speaker, and a timekeeper. In how many ways can these three roles be assigned to the 8 authors?

Answer 1

To assign three distinct roles to 8 authors, one calculates the number of permutations, resulting in 336 different ways to assign the roles.

Step-by-step explanation:

Calculating Combinations for Assigning Roles

The student has asked a combinatorial question: In how many ways can three roles (a moderator, a speaker, and a timekeeper) be assigned to 8 authors? This is a problem of permutations where order matters because the roles are distinct. To find the answer, use the permutation formula which in this case is P(n, k) = n! / (n-k)!, where n is the total number of items to choose from, and k is the number of items to choose.

Here, we have 8 authors (n=8) and we need to pick 3 of them (k=3). Plugging the values into the formula gives us:

P(8, 3) = 8! / (8-3)!

= 8! / 5! = (8×7×6) / (3×2×1)

= 336.

Hence, there are 336 different ways to assign the three roles to the 8 authors.