1 / 22

Use Combinations and the Binomial Theorem (continued)

Use Combinations and the Binomial Theorem (continued). Lesson 10.2 Algebra II. Agenda. Homework Review Continue discussion about combinations and binomial theorem. Homework: The rest of homework #3 from the assignment sheet Quiz on Friday lessons 10.1 – 10.2.

schuyler
Download Presentation

Use Combinations and the Binomial Theorem (continued)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Use Combinations and the Binomial Theorem (continued) Lesson 10.2 Algebra II

  2. Agenda • Homework Review • Continue discussion about combinations and binomial theorem. • Homework: The rest of homework #3 from the assignment sheet • Quiz on Friday lessons 10.1 – 10.2

  3. Use Combinations and the Binomial Theorem Formally… Combinations of n objects taken r at a time The number of combinations of r objects taken from a group of n distinct objects is denoted by DEFINITION SLIDE

  4. Use Combinations and the Binomial Theorem Let’s look at the problem b from the fake quiz… 3 scoops from 25 flavors in a bowl… Written as a combination…. EXAMPLE SLIDE

  5. Use Combinations and the Binomial Theorem Do problems 1 and 3 from Practice 10.2 B.

  6. Use Combinations and the Binomial Theorem Sometimes we have multiple events… For example.. Let’s say that we want to know how many different choices we would have to select from for a 2 scoop bowl and a 3 scoop bowl (from 25 flavors..). How would you figure that out? Example Slide

  7. Use Combinations and the Binomial Theorem

  8. example 2 from the book: William Shakespeare wrote 38 plays that can be divided into three genres; 18 are comedies, 10 are histories and 10 are tragedies. a. How many different sets of exactly 2 comedies and 1 tragedy can you read?

  9. example 2 from the book: William Shakespeare wrote 38 plays that can be divided into three genres; 18 are comedies, 10 are histories and 10 are tragedies. How many different sets of exactly 2 comedies and 1 tragedy can you read? i. To get started… how many combinations do you have of 2 comedies? ii. How many combinations do you have of 1 tragedies? iii. Can you use the counting principle?

  10. example 2 from the book: William Shakespeare wrote 38 plays that can be divided into three genres; 18 are comedies, 10 are histories and 10 are tragedies. b. How many different sets of at most 3 plays can you read? To answer this question we need to determine what is really being asked… at most means that we could read none, one, two or three… so it becomes the sum of each of those…

  11. example 2 from the book: William Shakespeare wrote 38 plays that can be divided into three genres; 18 are comedies, 10 are histories and 10 are tragedies. b. How many different sets of at most 3 plays can you read?

  12. Use Combinations and the Binomial Theorem Let’s try problems 12 and 13 on 10.2 practice B.

  13. Use Combinations and the Binomial Theorem Yesterday’s lesson focused on Pascal’s triangle and that the numbers in the triangle are the same as the number of combinations. From the homework last night’s homework you saw that when you expand binomials that the coefficients are the same as the numbers in Pascal’s triangle. So, can we use the combinatorial coefficients to expand binomials?

  14. Use Combinations and the Binomial Theorem So..

  15. Use Combinations and the Binomial Theorem Binomial Theorem: For any positive integer n, the binomial expansion of is: DEFINITION SLIDE

  16. Use Combinations and the Binomial Theorem Binomial Theorem: Find: EXAMPLE SLIDE

  17. Use Combinations and the Binomial Theorem When you have what do you notice about the signs? Write a sentence with you answer. When you have what do you notice about the signs? Write a sentence with you answer. CONCEPT SLIDE

  18. Use Combinations and the Binomial Theorem Do problems 15 and 16 from 10.2, practice B.

  19. Use Combinations and the Binomial Theorem You can also use the binomial theorem to find the coefficient in an expansion. Find the coefficient of in the expansion of … EXAMPLE SLIDE

  20. Use Combinations and the Binomial Theorem Summary of Lesson 10.2: Major Concepts – • Finding the number of combinations Where n is the number of objects available..(pizza toppings) and r is the number chosen (how many toppings on your pizza.) SUMMARY SLIDE

  21. Use Combinations and the Binomial Theorem Major Concepts Continued 2. The Binomial Theorem The number of combinations can be used for expanding a binomial. SUMMARY SLIDE

  22. Use Combinations and the Binomial Theorem Major Concepts Continued: 3. Pascal’s triangle Both the number of combinations and the coefficients for binomial expansions can be found in Pascal’s triangle. SUMMARY SLIDE

More Related