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Permutations and Combinations

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MDM 4U: Mathematics of Data Management

Unit: Counting and Probability

By: Mr. Allison and Mr. Panchbhaya

Permutations and Combinations

- 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

- Probability Video
- Review
- Worksheet
- Game show Activity

- 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

- 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

- Ordered arrangement of objects selected from a set
- Ordered arrangement containing a identical objects of one kind is

- Collection of chosen objects for which order does not matter

Speed Round: 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

- 455 ways
- 6 ways
- 2730 ways

- 151200
- 210
- 720

- 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

- 360
- 480
- 720
- 5040
- None of the above

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

- 5040
- 4536
- 2688
- 1470

- = 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

- = 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.

- 1400
- 1600
- 1800
- 1500

- 9 × 10 × 10 × 2 = 1800
- First # can’t be ‘0’
- Last # has to be ‘5’ or ‘0’

- 15,120
- 14,840
- 15,620
- 40,320

- 3* × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 15,120
- EOA are your 3 choices

- 990
- 1331
- 165
- 286

- C(11,3) 165

- 2,598,960
- 3,819,816
- 270,725
- 311,875,200

- C(52,5)

- 7,962,624
- 42,504
- 5,100,480
- 98,280

- C(24,5) 42,504

- 8
- 10
- 2
- 5

- = 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

- = 8 x 8 x 8 x 10 x 10 x 10 x 10
- = 5,120,000