Math 10 fundamental principle of counting
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This document discusses the fundamental counting principle (FCP) and provides examples of how to use it to solve problems. It begins by listing the 9 possible outcomes of a game of rock-paper-scissors. Two word problems are then presented that involve counting the number of possible outfits and 4-digit codes given constraints. The FCP is defined as stating that if one event can occur in m ways and a second in n ways, their combination is m*n. Several practice problems are worked out applying the FCP before students are evaluated on 5 multiple choice questions involving counting problems. Homework involves preparing another problem using the FCP.
Math 10 fundamental principle of counting
- 1. Fundamental Counting Principle THIRD QUARTER MATHEMATICS 10 ISAAC M. SUBELDIA Mathematics Teacher
- 2. Priming : Rock, Paper, Scissors
- 3. OBJECTIVES: • Identify the fundamental counting principle (FCP). • Answer exercises applying FCP. • Solves problems involving FCP.
- 4. LIST ALL THE POSSIBLE OUTCOME OF THE GAME ROCK, PAPER, SCISSOR Rock - Rock Rock - Paper Rock - Scissor Paper – Paper Paper – Scissor Paper - Rock Scissor – Scissor Scissor – Rock Scissor – Paper 9 possible outcome.
- 7. Together with your partner answer the following problems: Present your answer to the class. Problem 1 Victoria invited Nina to her birthday party. Nina has 4 new blouses (stripes, with ruffles, long-sleeved, and sleeveless) and 3 skirts (red, pink, and black) in her closet reserved for such occasions. • Assuming that any skirt can be paired with any blouse, in how many ways can Nina select her outfit? List the possibilities. • How many blouse-and-skirt pairs are possible? • Show the other way of finding the answer in item 1.
- 8. 3. What can you say about the list you made? Problem 2 Suppose Daniel secured his bike using combination lock. Later he realized that he forgot the 4-digit code. He only remembered that the code contains the digits 1, 3, 4, and 7. • List all the possible codes out of the given digits. • How many possible codes are there? • What can you say about the list you made?
- 9. Our canteen regularly prepares your snacks. This is also one source of our fund to support the need of our school. A meal consists of a bread, hot soup and beverage. How many different set of snack can be selected if there are 2 bread (Hamburger, Egg burger), 3 hot soup (sopas, sampurado, aruzcaldo) and 2 beverages (juice, mineral water) available?
- 10. Solution: 2 Bread x 3 soup x 2 beverages= 12 sets
- 11. The Fundamental Counting Principle states that if one event can occur m ways and a second event can occur n ways, the number of ways the two events can occur in sequence is m • n.
- 12. How many possible outcomes if you toss to coins?
- 16. Answers. 1. 3 x 2 x 1 = 6 2. 2 x 5 x 3 = 30 3. 4 x 4 x 4 x 4 x 4 = 1024
- 17. Application How many ways can you choose 6 numbers in a LOTTO? USING FPC 75 x 74 x 73 x 72 x 71 x 70 = 144, 978, 876, 000
- 18. GENERALIZATION Fundamental Counting Principle – states that if activity A can be done in n1 ways, activity B can be done in n2 ways, activity C in n3 ways, and so on, then activities A, B, and C can done simultaneously n1*n2*n….ways DID WE MEET OUR OBJECTIVES?
- 19. Evaluation Direction: Choose the letter of the correct answer 1 minute each question.
- 20. EVALUATION: Project 555 Direction: Read the problem carefully then choose the letter of the correct answer: 2 minutes each problem. Are you ready?
- 21. 1. Ben can take any one of three routes from school (S) to the town center (T), and can then take five possible routes from the town center to his home (H). He doesn't retrace his steps. How many different possible ways can Ben walk home from school? a. 7 b. 8 c. 15 d. 56
- 22. 2.Sarah goes to her local pizza parlor and orders a pizza. She can choose either a large or a medium pizza, has a choice of seven different toppings, and can have three different choices of crust. How many different pizzas could Sarah order? a. 12 b. 20 c. 27 d. 42
- 23. 3.Derek must choose a four-digit PIN number. Each digit can be chosen from 0 to 9. How many different possible PIN numbers can Derek choose? d a. 5,040 b. 6,541 c. 9,000 d. 10,000
- 24. 4.Jenny has nine different skirts, seven different tops, ten different pairs of shoes, two different necklaces and five different bracelets. In how many ways can Jenny dress up? a. 6,300 b. 7,560 c. 12, 600 d. 63,000
- 25. 5.A meal consists of a main dish, a side dish, and a dessert. How many different meals can be selected if there are 3 main dishes, 3 side dishes and 7 desserts available? a. 40 b. 63 c. 21 d. 27
- 26. Answer: 1. C 2. D 3. D 4. A 5. B
- 27. HOME WORK Prepare one problem involving Fundamental Principle of Counting with answer and solution.