Question

Alice, Bob, Carol, David, and Edward are being chosen for the positions
of president, vice president, secretary, treasurer, and publicity chair for their school’s math club. If each student can take at most two roles (any two roles are allowed, e.g. Alice is allowed to be both president and vice president), how many ways are there for the roles to be filled?

1. thienthi
The computation illustrated by the combination shows that the number of ways will be 60 ways that the roles can be filled.

### How to solve the number of ways?

From the information given, Alice, Bob, Carol, David, and Edward are being chosen for the positions of president, vice president, secretary, treasurer, and publicity chair for their school’s math club and each student can take at most two roles
It should be noted that based on the information given, This can be solved through permutations and combination. Permutations and combination implies the various ways that the objects from a set can be selected without replacement in order to be able to form subsets.
Therefore, the number of ways based on the information given will be:
= 5!/2!
= (5 × 4 × 3 × 2)/2
= 60 ways
Therefore, based on the information given above, it can be deduced that the there will be 60 ways that the roles can be filled.