EXAMPLE 3.2.10

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.

P(6, 3) = 6 factorial divided by (6 minus 3) factorial
= 6 factorial divided by 3 factorial
= 120

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) times (5) times (4) = 120