Algebra 1 Common Core Student Edition, Grade 8-9

Go t I t? 3. There are 6 students in a classroom with 8 desks. How many possible

seating arrangements are there?

A combinat ion is a selection of objects without regard to order. For example, if you are

selecting two side dishes from a list of five, the order in which you choose the side

dishes does not matter.

Key Concep t Combination Notation

The expression nCr represents the number of combinations of n objects chosen

r at a time.

r = w!

n r r\(n-r}\

Ex a m p l e 8C2 2[(8 _ 2), 2!g, ^ #. 5. 4. 3. 2. i) 28n 8! 8! _8-7-6-5’4»3-2-l

Do yo u u se a
permutation or a
combi nat ion?
The order of the people
on the jury does
not matter, so use a
combination.

Using Com b inat i on Not at ion

Multiple Choice Twenty people report for jury duty. How many different 12-person

juries can be chosen?

(3D 20 CD 240 CD 125,970 CD 479,001,600

You need the number of combinations of 20 jurors chosen 12 at a time. Find 20 ^ 12 -

20! 20!

2°Cl2 12!(20 — 12 )! 12! 8! Write using factorials.^

= 125,970 Sim plify using a calculator.

There are 125,970 different 12-person juries. The correct answer is C.

* Got It? 4. In how many different ways can you choose 3 types of flowers for a bouquet

from a selection of 15 types of flowers?

Lesso n Ch eck

Do yo u k n o w H OW?

Find the value of each expression.

1. 7! 2. 13! 3. 6P3


2. 10P4 5. 5C3 6. 7C3


3. How many outfits can you make with 6 shirts and
   4 pairs of pants?

MATHEMATICAL

Do y o u UN DERSTAN D? PRA CTI CES

@ 8. V o c a b u l a r y Would you use permutations or

combinations to find the number of possible

arrangements of 10 students in a line? Why?

© 9. Compare and Contrast How are permutations and

combinations similar? How are they different?

©10. Reasoning Explain why nCn is equal to 1.

rPo w er A l g eb r a.co m ^ Lesso n 12- 6 Per m u t at i o n s an d Co m b i n at i o n s^765

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