The president of a consulting firm wants to minimize the total number of hours it will take to complete four projects for a new client. Accordingly, she has estimated the time it should take for each of her top consultants-Charlie, Betty, Johnny, and Rick-to complete any of the four projects, as follows:
Assume there must be one-to-one matching between consultants and projects. In how many different ways can she assign these consultants to these projects?
A) 4
B) 8
C) 16
D) 24
E) 256

Question

The president of a consulting firm wants to minimize the total number of hours it will take to complete four projects for a new client. Accordingly, she has estimated the time it should take for each of her top consultants-Charlie, Betty, Johnny, and Rick-to complete any of the four projects, as follows: 
Assume there must be one-to-one matching between consultants and projects. In how many different ways can she assign these consultants to these projects?
A) 4 
B) 8 
C) 16 
D) 24 
E) 256

Quizplus · Accepted Answer

There are four consultants and four projects, so the first consultant can be assigned to one of the four projects, the second consultant can be assigned to one of the remaining three projects, the third consultant can be assigned to one of the remaining two projects, and the last consultant must be assigned to the remaining project. Therefore, the total number of ways to assign consultants to projects is 4x3x2x1 = 24. Therefore, the answer is D.

The President of a Consulting Firm Wants to Minimize the Total