Page 207 - Math Course 3 (Book 2)
P. 207
Permutations and Combinations
MO. 12 - L6b n! Definition of
C =
n r (n – r)!r! combination
Using Combinations 22! n = 22, r = 4
C =
22 4 (22 – 4)!4!
22!
= 18!4! 22 – 4 = 18
Vocabulary A-Z 1
Let us learn some vocabulary = 22 • 21 • 20 • 19 • 18 ! Divide by the GCF,
18!.
18! 4!
1
175, 560
= or 7315 Simplify.
combination 24
An arrangement or listing in which order is not
important is called a combination. Answer There are 7315 ways to pull 4
coins out of a bag of 22.
If you are choosing 2 salad ingredients from
a list of 10, the order in which you choose the There are two questions to consider.
ingredients does not matter.
• How many ways can 2 pennies be pulled from 10?
• How many ways can 2 nickels be pulled from 6?
Key Concept Using the Fundamental Counting Principle, the
answer can be determined with the product of the
two combinations.
Combination ways to choose ways to choose 2
2 pennies out nickels out
Words The number of combinations of n of 10 of 6
objects taken r at a time is the quotient
of n! and (n – r)!r!.
( C ) ● ( C )
2
10
2
6
Symbols C = n!
n r (n – r)!r! 10! 6! Definition of
( C )( C ) = •
10 2 6 2 (10–2)!2! (6–2)!2! combination
10! 6!
= • 4! 2! Simplify.
8! 2!
Let’s Begin Divide the first
term by its
10 • 9
= • 6 • 5 GCF, 8!, and the
2! 2! second term by
its GCF, 4!.
Combinations and Probability
= 675 Simplify.
Example There are 675 ways to choose this particular
combination out of 7315 possible combinations.
675
MONEY P(2 pennies, = 7315 ←number of favorable outcomes
2 nickels)
←number of possible outcomes
Diane has a bag full of coins. There are 10 pennies, 135
6 nickels, 4 dimes, and 2 quarters in the bag. How = 1463 Simplify
many different ways can Diane pull four coins out
of the bag?
The probability that Diane will
The order in which the coins are chosen does not Answer select two pennies and two
matter, so we must find the number of combina- nickels is , or about 9%.
135
tions of 22 coins taken 4 at a time. 1463
199