Page 201 - Math Course 3 (Book 2)

Counting Outcomes

Counting Arrangements
Bread Meat Side Item Outcomes
chips WSC
salami brownie WSB Example
fruit WSF
chips WTC There are 8 students in the Algebra Club at Central
wheat turkey brownie WTB High School. The students want to stand in a line
for their yearbook picture. How many different
fruit WTF ways can the 8 students stand for their picture?
chips WHC
ham brownie WHB The number of ways to arrange the students can
be found by multiplying the number of choices for
fruit WHF each position.
chips RSC
salami brownie RSB • There are eight people from which to choose for
the first position.
fruit RSF
chips RTC • After choosing a person for the first position,
rye turkey brownie RTB there are seven people left from which to choose
for the second position.
fruit RTF
chips RHC • There are now six choices for the third position.
ham brownie RHB • This process continues until all positions have
fruit RHF been filled.

The tree diagram shows that there The number of arrangements is:
Answer n = 8 • 7 • 6 • 5 • 4 • 3 • 2 • 1 or 40,320
are 18 possible combinations.

There are 40,320 different ways
Answer
they could stand.
Fundamental Counting Principle

Example Your Turn!

Tree Diagram
The Best Deal computer company sells custom
-made personal computers. Customers have a A lunch buffet offers a combination of a meat, a
choice of 11 different hard drives, 6 different key- vegetable, and a drink for $5.99. The choices of
boards, 4 different mice, and 4 different monitors. meat are chicken or pork; the choices of vegetable
How many different computers can a customer are carrots, broccoli, green beans, or potatoes; and
order? the choices of drink are milk, lemonade, or a soft
drink. Use a tree diagram to determine the number
Multiply to find the number of custom computers. of possible lunch combinations.

number of A. 12
hard drive keyboard mice monitor custom
choices choices choices choices computers B. 24
C. 30
11 ● 6 ● 4 ● 4 = 1056 D. 18

The number of different custom
Answer
computers is 1056.

193