Page 819 - Algebra 1

L E S S O N Solving Problems Involving Combinations 118
Warm Up
1. Vocabulary A ( permutation, factorial ) is an arrangement of
(111)
Simplify. 2. 7!
(111)
Simplify. 4. 7P3
(111)
outcomes in which the order does matter.
_ 3. 6! (111) 4!
5. 9P4 (111)
New Concepts In Lesson 111, you learned about permutations, a selection of items where order does matter. In some cases, however, the final group of items is all that
matters, not the order in which the items were selected. A combination is a grouping of items where order does not matter.
Comparing Combinations to Permutations
A teacher puts 4 essay questions on a test. They are labeled A, B, C, and D. Students are required to choose 3 questions to answer.
Example
1
a. How many permutations of the 3 questions are possible? SOLUTION
First, find the number of permutations.
_
= 4·3·2·1 =24.
_ 4P3 = 4! = 4!
(4 - 3)! 1!
1
There are 24 permutations of the 3 test questions.
b. How many combinations of the 3 questions are possible?
SOLUTION
As the order of the questions chosen does not matter, choosing ABC is
the same as ACB, CAB, CBA, BCA, and BAC. So, to find the number of combinations, list the 24 permutations and then cross out the duplicate sets.
Math Reasoning
Analyze Why are there more permutations than combinations?
ABC ABD ACB BAC BAD BCA CAB CAD CBA DAB DAC DBA
ACD ADB ADC BCD BDA BDC CBD CDA CDB DBC DCA DCB
804 Saxon Algebra 1
That leaves 4 combinations of the 3 test questions.