Algebra 1 Common Core Student Edition, Grade 8-9

Per m u t at i o n s an d

Co m b i n at i o n s

Object ive To find permutations and combinations

IP

Pr ep ar es f o r S-CP.B.9 Use perm ut at io ns and

combinations to compute probabilit ies of compound

events and solve problems.

MP 1, MP 2, MP 3, M P4, M P6

Co m m o n Co r e St at e St a n d a r d s

Read y!

Making a list

could t ak e a long

time. Is there a

f ast er way?

MATHEMATICAL

PRA CTI CES

iH

At an amusement park, you want to go on

all o f t h e rid es shown on t h e sig npost. I n

how many d i f f e r e n t o rd ers can you go on

the rides? Describe how you found the

answer.

Lesso n

Vocabulary

Multiplication

Co u n t i n g

Pr i n ci p l e

perm ut at ion

n factorial

co m b in at i o n

Essent ial Und er st and ing You can use counting methods to find the number of

possible ways to choose objects with and without regard to order.

One way to find the possible orders of objects is to make an organized list. Another

way is to make a tree diagram. Both methods help you see if you have thought of all

the possibilities.

The tree diagram below shows all the possible orders for watching three movies

(a comedy, a drama, and an action film).

First Movie

comedy

drama

act i on

Se c o n d M o v i e Th i r d M o v i e O r d e r o f M o v i e s

drama -------« action comedy, drama, action

act i on ------- 1 drama comedy, act ion, drama

comedy -------< act ion drama, comedy, act ion

act i on -------« c o m e d y d r a m a , a c t i o n , c o m e d y

comedy -------< drama act ion, comedy, drama

drama -------< c o m e d y act i on, dr ama, comedy

There are six possible orders for watching the three movies.

When one event does not affect the result of a second event, the events are independent.

When events are independent, you can find the number of outcomes using the

Multiplication Counting Principle.

762 Ch ap t er 12 Data Analysis and Probability