How many 4letter words can be made using the letters QUIP ...
[Pages:10]4_7Combinations.notebook
April 24, 2013
From yesterday's practice questions... How many 4letter "words" can be made using the letters QUIP?
How many 4letter "words" can be made using the letters QUIP if Q and U must be together? NOTE: Always deal with restrictions first
and "blocked" objects are considered one item
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4_7Combinations.notebook
April 24, 2013
How many different 6letter "words" can be made from the word OTTAWA?
At first glance we might think there are 6! different "words"
But there are multiples of some letters. We are not able to distinguish between one "T" and the other "T"
Since there are 2! ways to arrange the Ts and 2! ways to arrange the As, then there will be 2! x 2! duplicates.
To account for this overcounting we simply divide
6! / (2! x 2!) or 6! / (2!2!)
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4_7Combinations.notebook
April 24, 2013
Sometimes it is more efficient to use the COMPLEMENT
(All possible arrangements) (arrangements you don't want) = (arrangements you do want)
Brooklyn has 6 different coloured sweaters to pile up in her drawers.
How many ways can she stack them so that the red sweater is not
on the bottom?
Using Direct Reasoning
TIP Deal wit the restriction
The red sweater cannot b
sweaters that can be on the
Since there are 5 other sw we know the number of arra
Answer: 5 x 5! =
Using Indirect Reasoning ( All Red sweater on botto
If there were no restriction If the Red sweater was on
Red sweater NOT on the b
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4_7Combinations.notebook
April 24, 2013
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4_7Combinations.notebook
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Combinations
A permutation is an arrangement of objects that need to be in a particular order. (role/job/position)
A combination is an arrangement of objects that do NOT need to be in order.
Permutation example: Choosing a President and a Vicepresident from a group of 6 people solution: P(6,2) = 6! / (62)! = 6! / 4! = 6x5 = 30 possible arrangements
Combination example: Choosing two people for a committee from a group of 6 people
In this case if we choose Bob and Julie, it would be the same as choosing Julie and Bob (order is not important = "combination") If Bob and Julie were chosen as President and VicePresident, you can see that President Bob and VP Julie is not the same as President Julie and VP Bob. (specific roles = "permutation")
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4_7Combinations.notebook
April 24, 2013
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4_7Combinations.notebook
April 24, 2013
From a class of 30 students, determine the number of ways a 5 person committee can be selected to organize a class party.
a) with no restrictions Hint: Choose 5 people from a group of 30, no order
b) with Marnie on the committee HINT: Marnie must be included, so we are choosing
4 other people from the remaining 29, no order
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