EXAMPLE 1.5.13

Recall this problem from earlier: There are six greyhounds in a race: Spot, Fido, Bowser, Mack, Tuffy, William. How many different 1st-2nd-3rd place orders of finish are possible? We saw that the answer was P(6,3) = 120.

New question: After the race, three dogs will be randomly chosen for veterinary examination. How many different three-dog groups are possible?

SOLUTION

In this case, all we are concerned with is choosing three dogs; we don't care about the order in which the dogs are chosen or listed (for instance, if Tuffy, Spot, and Fido get the vet treatment, it's the same as if Fido, Spot, and Tuffy get the vet treatment; changing the order in which we list the three elements does not give a different outcome). The number of outcomes is the number of combinations of 6 things taken 3 at a time.