EXAMPLE 1.5.19

Gomer has eight pet wolverines. He has won a gift certificate to Wally's Wolverine World, that entitles him to one free wolverine massage, one free wolverine shampoo, and one free wolverine manicure. Gomer will randomly select which wolverines receive the treats described above.

1. How many different outcomes are possible, if we assume that no wolverine will receive more than one treat?

A. 512                         B. 256             C. 56               D. 336

 

 

2. How many different outcomes are possible, if we assume that it may be possible for a wolverine to receive more than one treat?

A. 512                         B. 256             C. 56               D. 336

 

SOLUTIONS

1.  He must select three different wolverines from a set of eight wolverines.  Since the three wolverines will receive different treatments, this is a permutation problem, not a combination problem.  (For example, if Fluffy gets the shampoo, Whiskers gets the manicure, and Angel gets the massage, thatÍs different from the case where Whiskers gets the shampoo, Angel gets the manicure, and Fluffy gets the massage; what matters here is not only which three wolverines are selected, but also which wolverine gets which treat.)

P(8,3) = 336

 

2.  In this case, since it is possible for wolverine to be selected for more than one gift, it is not a permutation problem or a combination problem (we arenÍt necessarily choosing a 3-element subset).  This means that we must use the FCP.

Gome needs to make 3 independent decisions:

1.  Who gets the massage?  8 options

2.  Who gets the manicure?  8 options

3.  Who gets the manicure?  8 options

 

(8)(8)(8) = 512