6th Grade Math Textbook, Fundamentals

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12-8

So there are 15 different ways to combine two paint colors

from six possible choices.

number of permutations of 2 paints

number of permutations of picking

2 paints from a group of 6

Combinations

Objective To determine the number of combinations of objects• To find permutations

and combinations using a graphing calculator

You and your friend Jesse are going to paint his
basement. His parents have six cans of leftover
paint in different colors that you can use. Jesse’s
parents suggest that you combine two colors to make a more
unusual color for the walls. How many different combinations
of two colors can be made from the six ready-made colors?

To solve this problem, you need to find the number of

different 2-color combinations.

A is a collection of objects or items in which

order does notmatter. In this problem, a blue-green paint

color is the same as a green-blue paint color. It does not

matter in which order the paints are chosen. They are

considered to be the same pair.

Here are two possible ways to solve this problem.

Method 1 Make an Organized List

Suppose the paint colors are Red (R), Yellow (Y),

Blue (B), Green (G), Violet (V), and White (W).

All possible outcomes are:

RY YR BR GR VR WR

RB YB BY GY VY WY

RG YG BG GB VB WB

RV YV BV GV VG WG

RW YW BW GW VW WV

In the organized list above, cross-out any repeated paint colors.

So there are 15 different 2-color combinations of paints.

Method 2 Use Permutations

To find the number of combinations,

• First find the number of permutations of picking two paints
  from a group of six.


• Then divide this number by the number of permutations
  of 2 paints to eliminate any duplicate combinations.

6 • 52! 2 • 1 (^30302 15)
combination
6 • 5 30 permutations