The Multiplication Rule for Counting
Liberal Arts Mathematics
Assignment Text
Answer the following problems from Section 7.1 of the textbook: 1 – 8.
For reference, the text of the problems are duplicated below.
An ice-cream parlor sells 26 different flavors of ice cream. A basic
sundae has one scoop of any flavor of ice cream, you choice of one of 3
sauces, and any one of 8 different toppings.
- How many different basic sundaes are possible?
- The ice-cream parlor also sells a medium sundae. The options are the
same except it starts with 2 scoops of ice cream, which can be the
same flavor or different flavors. How many different medium sundaes
are there?
- The ice-cream parlor also sells a large sundae. The choice of a
large sundae allows you to choose any 3 scoops of ice cream, any 2
sauces (they can be the same, or you can choose 2 different ones),
and any 3 toppings (that might be 3 servings of the same topping, or
2 servings of one topping and a single serving of another, or 3
different toppings). How many different large sundaes are possible?
- A company that builds custom computers offers 4 hard drive sizes, 4
memory sizes, 3 graphics cards, and 3 display options. How many
computer configurations do they offer, if customers choose one of
each customization?
- A video game allows user to customize their avatars. There are 12
hair styles that user may choose from, as well as 5 hair colors, 8
skin tones, 24 shirts, 12 pants, and 8 shoes. How many different
avatars are possible?
- A small company has 3 divisions: Sales, Research and Development,
and Manufacturing. One person from each division will be chosen to
create an advisory board for the management group. If there are 8
people in Sales, 15 in Research and Development, and 48 in
Manufacturing, how many different compositions of the advisory board
are possible?
- A multiple-choice quiz has 5 questions, each of which have 4
possible answers. How many different ways are there to respond to
this quiz?
- The teacher decides to make the quiz from above a little harder by
offering 5 responses on each of the 5 questions. How many ways are
there to respond to this quiz?
Answer Key
- 624
- 16224
- 80,990,208
- 144
- 1,105,920
- 5760
- 1024
- 3125
Student Feedback Templates
#1 should be 624 ( 26*3*8 )
#2 should be 16224 ( 26*26*3*8 )
#3 should be 80,990,208 ( 26*26*26*3*3*8*8*8 )
#4 should be 144 ( 4*4*3*3 )
#5 should be 1,105,920 ( 12*5*8*24*12*8 )
#6 should be 5760 ( 8*15*48 )
#7 should be 1024 ( 4*4*4*4*4 )
#8 should be 3125 ( 5*5*5*5*5 )