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MDM 4U: Mathematics of Data Management Unit: Counting and Probability By: Mr. Allison and Mr. Panchbhaya. Permutations and Combinations. Specific Expectations. Strand 2.1

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Permutations and combinations

MDM 4U: Mathematics of Data Management

Unit: Counting and Probability

By: Mr. Allison and Mr. Panchbhaya

Permutations and Combinations


Specific expectations
Specific Expectations

  • Strand 2.1

  • Recognize the use of permutations and combinations as counting techniques with advantages over other counting techniques

  • Strand 2.2

  • Solve simple problems using techniques for counting permutations and combinations, where all objects are distinct

Learning Goals

  • Make connections between, and learn to calculate various permutations and combinations

  • Learn to behave in class


Agenda of the day
Agenda of the Day

  • Probability Video

  • Review

  • Worksheet

  • Game show Activity



Real life examples
Real Life Examples itself back to the car?

  • Video game designers

    • to assign appropriate scoring values

  • Engineering

    • new products tested rigorously to determine how well they work

  • Allotting numbers for:

    • Credit card numbers

    • Cell phone numbers

    • Car plate numbers

    • Lottery


Factorials
Factorials itself back to the car?

  • The product of all positive integers less than equal or equal to n

    n! = n x (n – 1) x (n – 2) x … x 2 x 1

    5! =5 x 4 x 3 x 2 x 1 = 120


Permutations
Permutations itself back to the car?

  • Ordered arrangement of objects selected from a set

  • Ordered arrangement containing a identical objects of one kind is


Combinations
Combinations itself back to the car?

  • Collection of chosen objects for which order does not matter


Speed Round: itself back to the car?The sports apparel store at the mall is having a sale. Each customer may choose exactly two items from the list, and purchase them both. The trick is that each 2-item special must have two different items (for example, they may not purchase two T-shirts at the same time). What are all the different combinations that can be made by choosing exactly two items?


15 combinations are possible itself back to the car?


Q how many combinations are made if you were purchasing three items instead of two
Q – How many combinations are made if you were itself back to the car?purchasingthree items instead of two?


1 a club of 15 members choose a president a secretary and a treasurer in
1 itself back to the car?. A club of 15 members choose a president, a secretary, and a treasurer in

  • 455 ways

  • 6 ways

  • 2730 ways



3. A student has to answer 6 questions out of 12 in an exam. The first two questions are obligatory. The student has:

  • 5040

  • 210

  • 720


4. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done.

  • 564

  • 645

  • 735

  • 756

  • None of the above


5. In how many different ways can the letters of the word “LEADING” be arranged in such a way that the vowels

  • 360

  • 480

  • 720

  • 5040

  • None of the above


6. How many permutations of 4 different letters are there, chosen from the twenty six letters of the alphabet (repetition is not allowed)?


Answer
Answer chosen from the twenty six letters of the alphabet (repetition is not allowed)?

The number of permutations of 4 digits chosen from 26 is 26P4 = 26 × 25 × 24 × 23 = 358,800


How many paths are there to the top of the board
How many paths are there to the top of the board? chosen from the twenty six letters of the alphabet (repetition is not allowed)?


Answer1
Answer chosen from the twenty six letters of the alphabet (repetition is not allowed)?


How many 4 digit numbers can be made using 0 7 with no repeated digits allowed
How many 4 digit numbers can be made using 0-7 with no repeated digits allowed?

  • 5040

  • 4536

  • 2688

  • 1470


Answer2
Answer repeated digits allowed?

  • = 7x7x6x5 = 1470

  • First digit of a number can not be ‘0’


No postal code in Canada can begin with the letters D,F,I,O,Q,U, but repeated letters are allowed and any digit is allowed. How many postal codes are possible in Canada?

  • 11,657,890

  • 13,520,000

  • 14,280,000

  • 12,240,000


Answer3
Answer D,F,I,O,Q,U, but repeated

  • = 20x10x26x10x26x10 = 13,520,000

  • 20 choices for the first letter (26 - 6 that cannot be chosen. 10 choices for the digit (0-9).

  • 26 choices for the 3 position (2nd letter)

  • then 10 choice for the 4th position

  • Then 26 and 10 since you can again repeat numbers and letters.


Using digits 0 9 how many 4 digit numbers are evenly divisible by 5 with repeated digits allowed
Using digits 0 – 9, how many 4 digit numbers are evenly divisible by 5 with repeated digits allowed?

  • 1400

  • 1600

  • 1800

  • 1500


Answer4
Answer divisible by 5 with repeated digits allowed?

  • 9 × 10 × 10 × 2 = 1800

  • First # can’t be ‘0’

  • Last # has to be ‘5’ or ‘0’


How many ways can you arrange the letters in the word redcoats if it must start with a vowel
How many ways can you arrange the letters in the word REDCOATS if it must start with a vowel

  • 15,120

  • 14,840

  • 15,620

  • 40,320


Answer5
Answer REDCOATS if it must start with a vowel

  • 3* × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 15,120

  • EOA are your 3 choices


How many groups of 3 toys can a child choose to take on a vacation from a toy box containing 11 toys?

  • 990

  • 1331

  • 165

  • 286


Answer6
Answer vacation from a toy box containing 11 toys?

  • C(11,3) 165


If you have a standard deck of cards how many different hands exists of 5 cards
If you have a standard deck of cards how many different hands exists of 5 cards

  • 2,598,960

  • 3,819,816

  • 270,725

  • 311,875,200


Answer7
Answer hands exists of 5 cards

  • C(52,5)


The game of euchre uses only 24 cards from a standard deck. How many different 5 card euchre hands are possible?

  • 7,962,624

  • 42,504

  • 5,100,480

  • 98,280


Answer8
Answer How many different 5 card euchre hands are possible?

  • C(24,5) 42,504


Solve for n 3 n p 4 n 1 p 5
Solve for n How many different 5 card euchre hands are possible?3(nP4) =n-1P5

  • 8

  • 10

  • 2

  • 5


Answer9
Answer How many different 5 card euchre hands are possible?



Answer10
Answer boys and

  • = 3! x 3! + 3! x 3!

  • = 72


Laura has ‘lost’ Jordan’s phone number. All she can remember is that it did not contain a0 or 1 in the first three digits. How many 7 digit #’s are possible


Answer11
Answer remember is that it did not contain a

  • = 8 x 8 x 8 x 10 x 10 x 10 x 10

  • = 5,120,000


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