Page 771 - Algebra 1

Example
2
Simplifying Expressions with Factorials
a. Find 7!.
SOLUTION
7!
= 7 · 6 · 5 · 4 · 3 · 2 · 1 = 5040
_ b. Find9!.
SOLUTION
9! _
= 9 · 8 · 7 · 6 · 5 · 4 · 3 · 2 · 1 4!_ _ _
4·3·2·1
= 9 · 8 · 7 · 6 · 5 = 15,120
Write the factors of 7! and multiply.
Write the factors of 9! and 4!. Multiply.
4!
Exploration Finding Possibilities When Order is Important
a. On an index card, list all possible ways that the 4 colored ribbons can
be arranged.
b. On a second index card, list all possible ways that any two of the four colored ribbons can be arranged.
When choosing 3 of 8 contestants as finalists in a competition, order doesn’t matter. However, in naming a first, second, and third place from the 8 contestants, the order does matter. Since order is important it is a permutation.
Finding the Number of Permutations
a. Your school is running a recycling campaign in which 6 classes are competing to see who can collect the most recyclable materials. In how many ways can the classes finish in first through sixth place?
SOLUTION
Materials
• index cards
• 4 different colored ribbons
Permutation
The number of_permutations of n objects taken r at a time is given by the
n! formula nPr = (n-r)! .
Example
3
Caution
Remember that 0! is equal to 1, not 0.
756 Saxon Algebra 1
This is_a permutation of 6 things taken 6 at a time. nPr = n! Write the formula.
(n - r)! __
6P6 = 6! = 6! (6 - 6)! 0!
Simplify.
Writethefactorsof6!and0!. Multiply.
= 6·5·4·3·2·1 __
= 720
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