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