Algebra 1 Common Core Student Edition, Grade 8-9

Key Concept Multiplication Counting Principle

Pr o b l em 1 Using the M ultiplication Counting Principle

Shopping Use the diagram below. How many ways are there to get from the first

floor to the third floor using only escalators?

W h a t is a n o th e r
way to solve this
problem?
You can draw a diagram
like the tree diagram
on the previous page to
show all of the possible
escalator routes.

If there are m ways to make a first selection and n ways to make a second selection,

then there are m • n ways to make the two selections.

Ex a m p l e

For 5 shirts and 8 pairs of shorts, the number of possible outfits is 5 • 8 = 40.

Ro u t es b y e sca l at o r f r o m

Ro u t es b y escal at o r f r o m (^) , first floor to third floor.... J
seco n d f l o o r t o t hi r d f l oor
Ro u t es b y escal at o r f r o m
first floor to second floor
There are 6 possible ways to get from the first floor to the third floor using
only escalators.
Go t I t? 1. a. A pizza shop offers 8 vegetable toppings and 6 meat toppings. How
many different pizzas can you order with one meat topping and one
vegetable topping?
b. Reasoning Is a tree diagram a convenient way to find the answer to
part (a)? Explain.
A permutation is an arrangement of objects in a specific order. Here are the possible
permutations of the letters A, B, and C without repeating any letters.
ABC ACB BAC BCA CAB CBA

lnl j Lesson 12-6 Perm ut at i ons and Com b in at i ons
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