2. How many ways can a baseball manager
arrange a batting order of 9 players?
Possibilities for 1st batter = 9
Possibilities for 2nd batter = 8
Possibilities for 3rd batter = 7
9*8*7*6*5*4*3*2*1 = 9! = 362,880
5. A store manager wishes to display 8
different brands of shampoo in a row. How
many ways can this be done?
Possibilities for 1st bottle = 8
Possibilities for 2nd bottle = 7
Possibilities for 3rd bottle = 6
8*7*6*5*4*3*2*1 = 8! = 40,320
8. The call letters of a radio station must
have 4 letters. The first letter must be a K or
W. How many different station call letters
can be made if repetitions are not allowed?
Possibilities for 1st letter = 2 {K, W}
Possibilities for 2nd letter = 25 (any letter other than your 1st letter)
Possibilities for 3rd letter = 24 (any letter other than 1st or 2nd)
Possibilities for 4th letter = 23 (any letter other than 1st ,2nd, or 3rd)
2*25*24*23 = 27,600
8. The call letters of a radio station must
have 4 letters. The first letter must be a K or
W. How many different station call letters
can be made if repetitions are allowed?
Possibilities for 1st letter = 2 {K, W}
Possibilities for 2nd letter = 26 (any letter)
Possibilities for 3rd letter = 26 (any letter)
Possibilities for 4th letter = 26 (any letter)
2*26*26*26 = 35,152
10. How many different ways can 9 trophies
be arranged on a shelf?
Possibilities for 1st trophy = 9
Possibilities for 2nd trophy = 8
Possibilities for 3rd trophy = 7
9*8*7*6*5*4*3*2*1 = 9! = 362,880
13. Evaluate each of these:
a. 8! 40,320
b. 10! 3,628,800
c. 0! 1
d. 1! 1
e. 7P5 2,520
f. 12P4 11,880
g. 5P3 60
h. 6P0 1
i. 5P5 120
j. 6P2 30
18. How many different ways can a city
building inspector visit 6 buildings in the city
if she visits them all in 1 day?
Possibilities for 1st building = 6
Possibilities for 2nd building = 5
Possibilities for 3rd building = 4
6*5*4*3*2*1 = 6! = 720
23. How many different ways can 4 tickets
be selected from 50 tickets if each ticket
wins a different prize?
Permutation
n = 50 tickets
r = 4 different prizes
50P4
= 5,527,200
24. How many different ways can a
researcher select 5 rats from 20 rats and
assign each to a different test?
Permutation
n = 20 rats
r = 5 different tests
20P5
= 1,860,480
28. How many ways can 3 cards be selected
from a standard deck of 52 cards
disregarding the order of selection?
Combination
n = 52 cards
r = 3 cards
52C3
= 22,100
38. Wake Up cereal comes in 2 types, crispy
and crunchy. If a researcher has 10 boxes of
each, how many ways can she select 3 boxes
of each for a quality control test?
Cripsy: Combination
n = 10 boxes
r = choosing 3 boxes
10C3
= 120
10C3
Crunchy: Combination
n = 10 boxes
r = choosing 3 boxes
10C3
* 10C3 = 120*120 = 14,400
= 120