EXAMPLE 1.5.22

Is it     A. P(8,3);        B. C(8,3);       C. 83; or          D. 38 ?

There are 8 kittens in a pet shop:

1. Three kittens will be randomly selected and donated to a nursing home. How many different three-kitten collections are possible?

2. One kitten will be chosen for a rabies vaccination, one kitten will be chosen for a distemper shot, and one kitten will be declawed. In how many different ways can the choice of kittens be made, if it is possible that more than one of these treatments may be given to the same kitten?

3. One kitten will be chosen for a rabies vaccination, another kitten will be chosen for a distemper shot, and a third kitten will be declawed. In how many different ways can the choice of kittens be made?

4. Each kitten will be given either a red, blue, or green ribbon. How many outcomes are possible?

 

SOLUTION

1.  We are choosing 3 different kittens from a set of 8 kittens.  Since the 3 kittens all receive the same reward, order isnÍt important.  This is a combination problem.  The answer is B.

 

2.  Since it is possible for the same kitten to be selected more than once, this problem doesnÍt involve permutations or combinations.  We use the FCP, with three independent decisions:

i.  Who gets the rabies vaccine?  8 options

ii.  Who gets the distemper shot?  8 options

ii.  Who gets declawed? 8 options

(8)(8)(8) = 83  The answer is C.

 

3.  We are choosing 3 different kittens from a set of 8 kittens.  Since the three kittens are receiving different treatments, this is a permutation problem, not a combination problem.  The number of outcomes is P(8,3).  The correct choice is A.

 

4.  We need to make 8 decisions (note: we are assuming that the 8 kittens are distinguishable from one another).

i.  What color ribbon does the first kitten get?  3 options

ii.  What color ribbon does the second kitten get?  3 options

iii.  What color ribbon does the third kitten get?  3 options

iv.  What color ribbon does the fourth kitten get?  3 options

v.  What color ribbon does the fifth kitten get?  3 options

vi.  What color ribbon does the sixth kitten get?  3 options

vii.  What color ribbon does the seventh kitten get?  3 options

vii.  What color ribbon does the eighth kitten get?  3 options

(3) (3) (3) (3) (3) (3) (3) (3) = 38   The answer is D.