EXAMPLE 1.5.10

There are six greyhounds in a race: Spot, Fido, Bowser, Mack, Tuffy,William.

We are concerned about who finishes first, second and third. How many different 1st-2nd-3rd orders of finish are possible?

Examples:

S-B-F

M-B-S

T-W-M

M-T-W

A. 120

B. 216

C. 18

D. 15

SOLUTION

The answer is going to be the number of permutations of 6 things taken 3 at a time, since a 1st-2nd-3rd place order of finish is determined by choosing three of the dogs and arranging them according to who finishes in which place.

We could also have gotten this answer by using the Fundamental Counting Principle, since writing down a typical order of finish requires that we make three dependent decisions.

(6)(5)(4) = 120