EXAMPLE 1.4.13

Homer, Gomer, Plato, Euclid, Socrates, Aristotle, Homerina and Gomerina form the board of directors of the Lawyer and Poodle Admirers Club. They will choose from amongst themselves a Chairperson, Secretary, and Treasurer. No person will hold more than one position. How many different outcomes are possible?

A. 336

B. 24

C. 512

D. 21

SOLUTION

Choosing a Chairperson, Secretary and Treasurer from among these 8 people requires us to make three decisions. However (unlike in all of the previous examples) these three decisions are not independent. For instance, the choice we make when we select the chairperson affects which options are available when we go to choose the Secretary, since the person selected to be Chairperson cannot also be selected to be Secretary.

i. Choose Chairperson: 8 options;

ii. Choose Secretary: 7 options (one person has already been chosen to be Chairperson);

iii. Choose Treasurer: 6 options (two people have already been chosen to be Chairperson and Secretary, respectively).

According to the Fundamental Counting Principle the number of outcomes is:

(8)(7)(6) = 336.