Question

in how many ways can a club schedule one member to work in the office on each of 4 different days, assuming members can work more than one day.
n = {bob, tim, alan, bill, cathy, david}
way(s)
(simplify your answer.)

Explanation:

Step1: Identify the problem type

This is a permutation with repetition problem. For each of the 4 days, we can choose any of the 6 members (since members can work more than one day).

Step2: Use the multiplication principle

For the first day, we have 6 choices. For the second day, we also have 6 choices (because a member can work again), same for the third and fourth days. So the total number of ways is calculated by multiplying the number of choices for each day. The formula for permutations with repetition is \(n^r\), where \(n\) is the number of items to choose from and \(r\) is the number of times we are choosing. Here, \(n = 6\) (the number of members) and \(r = 4\) (the number of days).
So the calculation is \(6^4\).

Step3: Calculate \(6^4\)

\(6^4=6\times6\times6\times6 = 1296\)

Answer:

1296