ICT role in 21st century education and its challenges
12.5 permutations 1
1. Lesson 12.5, For use with pages 675-679
1. Choose one of 4 friends, one of 4 restaurants,
and one of 3 meeting times.
Use the counting principle to find the number of
possible choices.
You NEED a scientific
calculator TODAY!
2. How many seven digit phone numbers are
possible if the first digit cannot be a 0?
2. Lesson 12.5, For use with pages 675-679
1. Choose one of 4 friends, one of 4 restaurants,
and one of 3 meeting times.
ANSWER 48
Use the counting principle to find the number of
possible choices.
You NEED a scientific
calculator TODAY!
2. How many seven digit phone numbers are
possible if the first digit cannot be a 0?
ANSWER 9 x 10 x 10 x 10 x 10 x 10 x 10 = 9,000,000
4. Essential Questions
• What are the differences between
permutations and combinations?
• What are the differences between odds
and probability?
• How is probability used to make
predictions?
• What are the differences between
experimental and theoretical probabilities?
5. • When looking at options or choices, we
often look at the arrangement, or order, of
people, letters, numbers, etc.
A permutation is an arrangement in
which ORDER is important.
Arranging “ABC” is different than “ACB”
6. • Let’s look at the three letters – A, B, C
• How many different ways can I arrange or
order these letters?
• What if I add “D” to the list? Now, how
many different arrangements?
7. • Let’s look at the three letters – A, B, C
• How many different ways can I arrange or
order these letters?
• What if I add “D” to the list? Now, how
many different arrangements?
6 ways
24 ways
8. EXAMPLE 1 Counting Permutations
Music
You have five CDs. You can use the counting principle
to count the number of permutations of 5 CDs. This is
the number of different orders in which you can listen
to the CDs.
Choices for
1st CD
Choices for
2nd CD
Choices for
3rd CD
Choices for
4th CD
Choices for
5th CD
5 4 3 2 1
ANSWER
You can listen to the CDs in 120 different orders.
= 120
9. Swimming Event
• There are 8 lanes for the swimming event. If
the top 2 swimmers are assigned to lanes 3,
and 4 in how many ways can the other 6
swimmers be assigned to their lanes?
• (Hint: -- you are only looking at 6 lanes)
• For the first of the remaining 6 swimmers, there are 6
possible lanes assignments. Once a selection has been
made, there are only 5 lanes left from which to assign the
next swimmer. After the second swimmer is assigned,
there are only 4 lanes left, and so on.
• 6 x 5 x 4 x 3 x 2 x 1 = 720 ways
10. • Factorial Notation is used to write the
product when the factors are consecutive
whole numbers.
• 4 factorial is written as 4! and it means
4 x 3 x 2 x 1 or 24
Find the factorial key on your calculator.
14. EXAMPLE 3 Evaluating a Permutation
Poetry
Two students are chosen from a group of 6 to read the
first and second poems at the school’s poetry reading.
To find how many different ways the students can be
chosen, find 6P2.
6P2
– == 6!
(6 2)!
6!
4!
Use permutation formula.
=
6 5 4 3 2 1
4 3 2 1
Divide out common factors.
= 30 Multiply.
ANSWER
The students can be chosen in 30 ways.
Using the counting principle we would have found it
by taking 6 x 5 = 30
15. • From the 9 players in the batting order, in
how many ways can a baseball manager
choose and order
the first 3 batters?
• 9 x 8 x 7 = 504 or 9P3 = 504
• the first 4 batters?
• 3024 ways
the first 5 batters?
15,120 ways
16. • There are 10 candidates for student
government. There are 4 different
positions. In how many ways can the
student government be chosen?
• 10P4 = 5040 ways
• Remember: these examples all involve
ORDER – arrangements / permutations
17. On Line Calculators
• Permutations and Combinations
– http://www.calctool.org/CALC/math/probability
/combinations
– http://www.mathsisfun.com/combinatorics/co
mbinations-permutations-calculator.html
• Factorials
– http://joemath.com/math124/Calculator/factori
al.htm
• www.lewiscentral.k12.ia.us/shipp
