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?
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.