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Counting Principle

Explore the fundamentals of counting principles using deck of cards and outfit selection scenarios. Discover permutations, combinations, factorials, and more. Practice applying counting rules to real-life situations. Engage in group discussions and activities to enhance learning.

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Counting Principle

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  1. Counting Principle Warm UP: List down what make up of a deck of cards. Name what you know about a deck of cards.

  2. Deck of Cards • 4 suits • 2 Black Suits (Clubs and Spades) • 2 Red Suits (Diamonds and Hearts) • 52 Cards • Each Suit (13 cards): Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, King, and Queen. • Face Cards: Jack, King and Queen

  3. Idea of the day • When do I use the counting principle?

  4. Investigation:How many choices do I have? • In the morning I realize that I have 5 different shirts to choose from. I also have 3 pairs of pants that match those shirts and 2 pairs of shoes. • Determine how many different outfits I have by making a tree diagram

  5. Investigation:How many choices do I have? • Suppose I have 3 face cards and 5 others. • Determine how many different sets of two cards I have from each of the categories by making a tree diagram

  6. Investigation:How many choices do I have? • Suppose I want to customize my license plate with 3 different numbers. • Determine how many different set of numbers I can have by making a tree diagram • What if the number on my plate can be repeated

  7. Group Discussion • Number student from 1-3 • At their group they are to answer: • What pattern did you notice? • What can you conclude about the counting principle rule?

  8. Ambassador Game: • Tell your partner what did you do for entertainment last night • Alphabetize your activity • The person who’s ______________ and ___________ go to a different group • Then discuss what you’ve discover to see if you all are in agreement with your conclusion

  9. Different Methods • There are 3 methods for calculating the number of possible outcomes for a sequence of event. • Counting Rules • Permutation Rules • Combination Rule

  10. Counting Principle: • Suppose that two events occur in order. If the first can occur in “m” ways and the second in “n” ways (after the first has occurred), then the two events can occur in order in m x n ways. • Order is extremely important for the counting principle. • In simple words, multiply the number of possibilities for each individual event

  11. Factorial:

  12. Examples: • At Brusters Ice-Cream you can get a regular cone, a sugar cone, or a waffle cone. If Bruster’s has 25 flavors how many one scoop ice-cream cones can you get? • 3 * 25 = 75 • How many two scoop cones can you get (assume that the second scoop must be different) • 3 * 25 * 24 = 1800

  13. Examples: • In NC, automobile license plates display 3 letters followed by four digits. How many license plates can be produced if repetition of letters and numbers are allowed? • 26 * 26 *26 = 17576 • What if repetition is not allowed? • 26*25*24 = 15600

  14. Example: • At the Olympics 8 runners race in the 100 m dash. In how many ways can they finish? • 8·7·6·5·4·3·2·1 • How else could we write this? • 8!

  15. Now you try: • A restaurant offers 6 main course, eight beverages and 3 desserts, how many different dinner options do they have? • A red die, a blue die and a white die are rolled, how many different outcomes are possible? • A company has 2844 employees. Each employee is to be given an ID number that consist of one letter followed by two digits. Is it possible that each employee has an individual ID?

  16. Answers • 6 * 8 * 3 = 144 • 6*6*6 =216 • 26 * 10 * 10 = 2600 • NO because you need 2844

  17. Deck of Cards Example • Two cards are chosen in order from a deck of cards. In how many ways can this be done if the first card is red and the second card is a club? • 26*13 = 338 • What if both cards are red? • 26*25 = 650 • What if both cards are Kings? • 4 * 3 = 12 • What if the first is a Queen and the second is a nine? • 4 * 4 = 16

  18. Runners Choice • In how many different ways can a race with six runners be completed? Assume there is no tie • 6*5*4*3*2*1=720

  19. ID Card: • The digit 0,1,2,3 and 4 are to be used in a 4 digit ID card. • How many cards are possible if repetition allowed? • 5*5*5*5=625 • What if repetition are not allowed? • 5*4*3*2=120

  20. Revisiting the EQ: • When do I use the counting principle?

  21. Group work: Section 13.1 • Pg 879-881: 2 – 36 even

  22. Homework 13.1 • Counting Rules Homework

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