Permutations-and-Combination introduction.ppt

Math Class 11

1. Permutation and Combination
Statistics CIE 9709/06

2. Permutations, Combinations &
Counting Principle
Essential Questions: Essential Questions:
What’s the difference between a What’s the difference between a
permutation & combination?permutation & combination?
When do we use the counting When do we use the counting
principle?principle?
Can you find the total number of Can you find the total number of
outcomes?outcomes?

3. •Permutation or Combination You Decide!
My fruit salad contains grapes, pineapples,
strawberries, and blueberries.
•Does it matter what order I place the
ingredients in the bowl?
•Which one is it?

4. •It is a Combination
•The order that you put the fruit in the fruit
salad does not matter so you do not count the
repeated events.
•So grapes, pineapple, strawberries,
blueberries is the same as blueberries,
strawberries, pineapple, grapes.

5. •Permutation or Combination You Decide!
•My locker combination is 23-5-17.
•Does it matter what order I turn the numbers?
•Which one is it?

6. •It is a permutation.
•Another set of numbers in a different order
will not open your locker so the order DOES
matter.
•So 23- 5 - 17 is very different that 23 - 17 - 5
or any other set of these 3 numbers.

7. •Counting Principle – involves outcomes with
different categories similar to a tree diagram.
•Example: You are making a password for your
computer. You will use 2 letters and 1
number, repeats are allowed.
•You have different categories:
•Letter • Letter • Number
•26 • 26 • 10 = 6760 outcomes possible

10. YOU TRY!
1)How many ways can 7 students finish a race in
1
st
, 2
nd
, and 3
rd
place?
First decide if the order matters or not. Then
calculate.

12. 2) How many ways can you order a white,
chocolate, or yellow cake, with chocolate or
vanilla icing, and 20 possible designs on top?
First think about what kind of problem this is.
Are there different categories or not? Does the
order matter?

13. 2) This uses the counting principle because
there are 3 different categories involved: the
type of cake, type of icing, and the type of
design.
3 • 2 • 20 = 120 possible outcomes

14. 3)How many ways can you arrange 3 sweaters
in a display window from 8 sweaters?
First decide whether the order matters. Then
calculate.

16. •Permutation (counting principle) example
without replacement.
You are creating a password with 4 digits. You
cannot repeat a number, how many possible
arrangements are there?
There are 10 digits, so start with that and each
other digit will go down by one.
So 10 • 9 • 8 • 7 = 5040 possible outcomes