Transcript Aim: What is a permutation? - Holy Angels Regional School

Aim: What is a permutation?
1.
Do Now:
Evaluate n(n -1)(n-2)(n-3).
n=5
2. n = 10
Vocabulary
• Permutation – an arrangement or listing in
which order is important
• Factorial – the product of all counting
numbers beginning with the number given
(n) and counting backward to 1
Example 6! = 6 × 5 × 4 × 3 × 2 × 1
Finding a permutation
An ice cream shop has 31 flavors. Carlos
wants to buy a 3-scoop sundae. How
many different arrangements can he make
if order is important?
29
31 × ______
30 × ______
______
# of
possible
flavors
for the
first
scoop
# of
possible
flavors
for the
second
scoop
# of
possible
flavors
for the
third
scoop
Using Permutation Notation
An ice cream shop has 31 flavors. Carlos
wants to buy a 3-scoop sundae. How
many different arrangements can he make
if order is important?
P(31, 3) = 31 × 30 × 29
or
31P3 = 31 × 30 × 29
Factorials
• A factorial is a specific type of permutation
in which an arrangement is made from all
members of the set
4! = P(4,4) = 4 × 3 × 2 × 1
OR
4! = 4P4 = 4 × 3 × 2 × 1
Practice
Evaluate.
1. P(5,2)
2. 8P4
3. How many possibilities can you arrange
all letters in the word math.
4. If six people are running a race, how
many different arrangements can there
be to award a 1st, 2nd, and 3rd place prize?