COURSE 2 LESSON 12-7
Combinations
You have one pen in each of these
colors: red, green, blue, and purple. You lend
three to a friend. How many combinations of
colors are possible in the pens you lend?
Color
red
Letter
r
green
blue
purple
g
b
p
Step 1 Let letters represent the four colors. Make an organized list of all
possible permutations.
(r, g, b)
(r, g, p)
(r, b, g)
(r, b, p)
(r, p, g)
(g, r, b)
(g, r, p)
(g, b, r)
(g, b, p)
(g, p, r)
(b, r, g)
(b, r, p)
(b, g, r)
(b, g, p)
(b, p, r)
(p, r, g)
(p, r, b)
(p, g, r)
(p, g, b)
(p, b, r)
(r, p, b)
(g, p, b)
(b, p, g)
(p, b, g)
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COURSE 2 LESSON 12-7
Combinations
(continued)
Step 2 Cross out the groups containing the same letters.
(r, g, b)
(r, g, p)
(r, b, g)
(g, r, b)
(g, r, p)
(g, b, r)
(b, r, g)
(b, r, p)
(b, g, r)
(p, r, g)
(p, r, b)
(p, g, r)
(r, b, p)
(r, p, g)
(r, p, b)
(g, b, p)
(g, p, r)
(g, p, b)
(b, g, p)
(b, p, r,)
(b, p, g)
(p, g, b)
(p, b, r)
(p, b, g)
Four different combinations of three colors are possible.
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COURSE 2 LESSON 12-7
Combinations
The county fair has 10 rides. You have time for 3 of them.
How many different combinations of rides are available to you?
Step 1 Find the total number of permutations.
10

first
choice
9

second
choice
8
= 720 permutations
Use the counting
principle.
third
choice
Step 2 Find the number of permutations of the smaller group.
3

2

1
= 6 permutations
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Use the counting
principle.
COURSE 2 LESSON 12-7
Combinations
(continued)
Step 3 Find the number of combinations.
total number of permutations
number of permutations of smaller group
=
720
6
= 120
There are 120 combinations of rides available.
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Divide.
Simplify.
COURSE 2 LESSON 12-7
Combinations
Find the number of combinations.
1. You choose 3 out of 6 people.
20
2. Any two letters from the set of letters C, D, S, T, and U.
10
3. Any three letters from the set of letters A, B, C, and D.
4
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