pencil, highlighter, GP notebook, textbook, calculator

1. total: pencil, highlighter, GP notebook, textbook, calculator U11D3 Have out: Bellwork: Start IC – 34 on the worksheet. IC – 34 personal identification number To choose a PIN (__________ _____________ ________) at a certain bank, you select 4 numbers from the digits 0 – 9, with no repeats. How many are possible? Make a decision chart to help you determine the answer.

2. total: IC – 34 Factorials to Permutations personal identification number To choose a PIN (__________ _____________ ________) at a certain bank, you select 4 numbers from the digits 0 – 9, with no repeats. How many are possible? Make a decision chart to help you determine the answer. +2 +2 10 9 8 7 _____ _____ _____ _____ = 5040 7 This looks like the beginning of 10!, but only down to _____, so the _____ is divided out. _____ _____ _____ _____ = 6! 10 9 8 7 So there are 4 spots to fill and 10 options to start with. How can I get a 6 out of this? 10 – 4 = 6

3. IC – 35 You’ve won 14 trophies since grade school. Your mom says that only 3 trophies can go on the mantle. In how many ways can you choose and arrange them? 14 13 12 2184 _____ _____ _____ = 12 This looks like the beginning of 14!, but only down to _____ with _____ divided out. _____ _____ _____ = 11! 14 13 12 So there are 3 spots to fill and 14 options to start with. How can I get an 11 out of this? 14 – 3 = 11

4. IC – 36 Solve the following problems. Use factorials to express each of the following solutions. • Fifty–two women vie for the “Miss USA” crown. In how many ways can a winner and her three runner–ups be chosen? 52 51 50 49 _____ _____ _____ _____ = 6,497,400 How can I write this as factorials? 52 – 4 = 48

5. Try b and c in your groups! b) The ECHS volleyball team is sponsoring a mixed–doubles sand court volleyball tournament and sixteen pairs have signed up for the chance to win one of the seven trophies and cash prizes. In how many ways can the teams be chosen and arranged for the top seven slots? • Carmen is getting a new locker at school and the first thing she must do is decide on a new combination. The three number combination can be picked from the numbers 0 – 35. How many different locker combinations could she make up if none of the numbers can be repeated?

6. IC – 36 b) The ECHS volleyball team is sponsoring a mixed–doubles sand court volleyball tournament and sixteen pairs have signed up for the chance to win one of the seven trophies and cash prizes. In how many ways can the teams be chosen and arranged for the top seven slots? Remember, each pair is one entity. 16 15 14 13 12 11 10 _____ _____ _____ _____ _____ _____ _____ = 57,657,600 How can I write this as factorials? 16 – 7 = 9

7. IC – 36 • Carmen is getting a new locker at school and the first thing she must do is decide on a new combination. The three number combination can be picked from the numbers 0 – 35. How many different locker combinations could she make up if none of the numbers can be repeated? 36 35 34 42,840 _____ _____ _____= 36?! But it only went to 35! Oh, 0 – 35 is 36 different numbers. How can I write this as factorials? 36 – 3 = 33

8. PERMUTATIONS Per around perimeter periscope “_______” means ________, as in __________ or _________. Mutation change “__________” means __________. Problems where we are concerned about order and arrangements are called ________________. permutations For example, the 6 arrangements of the letters ABC are permutations. Purrrrrr! The two main characteristics of a permutation are _____ ____________ and __________ matters. NO REPETITION ORDER

9. There are two important questions we must ask from here on out. 1) Does order matter? 2) Are repeats allowed? Here is a flowchart to help you out. We will fill in the rest when we talk about combinations. Does order matter? NO YES Are repeats allowed? Are repeats allowed? NO YES NO YES __________ (Leave blank) Combination Permutation Decision Chart

10. Practice: Determine whether or not the given situations are permutations or not.

11. Practice: Determine whether or not the given situations are permutations or not. Permutation Not a permutation Does order matter? NO YES Are repeats allowed? Are repeats allowed? NO YES NO YES Combination Decision Chart Permutation

12. Try c, d, e, and f in your groups! Does order matter? NO YES Are repeats allowed? Are repeats allowed? NO YES NO YES Combination Permutation Decision Chart

13. Practice: Determine whether or not the given situations are permutations or not. Permutation Not a permutation Does order matter? NO YES Are repeats allowed? Are repeats allowed? NO YES NO YES Combination Decision Chart Permutation

14. Practice: Determine whether or not the given situations are permutations or not. Not a permutation Permutation Does order matter? NO YES Are repeats allowed? Are repeats allowed? NO YES NO YES Combination Decision Chart Permutation

15. PERMUTATION NOTATION selecting arranging nPr is the notation for _________ and _________ r things from n things. Add nPr to the flowchart. Does order matter? NO YES Are repeats allowed? Are repeats allowed? NO YES NO YES ___________ (Leave blank) Combination Permutation Decision Chart nPr

16. Eight people are running a race. In how many different ways can they come in first, second, and third? IC – 38 things you are choosing from n = # of ______________________________ r = # of ______________________________ things you are choosing 8 For this problem, n = ____ and r = ____ 3 _____ =

17. Flip your worksheet over. Let’s go back and solve IC 34 – 36 using permutations this time. IC – 34 To choose a PIN at a certain bank, you select 4 numbers from the digits 0 – 9, with no repeats. How many are possible? We going to select and arrange 4 numbers from a group of 10 possible numbers. 10P4 = = 5040 IC – 36 • Fifty–two women vie for the “Miss USA” crown. In how many ways can a winner and her three runner–ups be chosen? We going to select and arrange 4 women from a group of 52 women. 52P4 = = 6,497,400 Try parts (b) and (c) on your own.

18. IC – 36 b) The ECHS volleyball team is sponsoring a mixed–doubles sand court volleyball tournament and sixteen pairs have signed up for the chance to win one of the seven trophies and cash prizes. In how many ways can the teams be chosen and arranged for the top seven slots? We going to select and arrange 7 teams from a group of 16 possible teams. 16P7 = = 57,657,600 • The three number combination can be picked from the numbers 0 – 35. How many different locker combinations could be made up if none of the numbers can be repeated? We going to select and arrange 3 numbers from a group of 36 possible numbers. 36P3 = = 42,840

19. Ice Cream Shop Try the Ice Cream problem in your groups!

20. You go to 31 flavors Ice Cream. Determine the number of ways you can order the following on an ice cream cone. 31 31 31 = 961 Does order matter? NO YES Are repeats allowed? Are repeats allowed? NO YES NO YES Combination Permutation Decision Chart nPr

21. You go to 31 flavors Ice Cream. Determine the number of ways you can order the following on an ice cream cone. 31 31 31 = 29,791 Does order matter? NO YES Are repeats allowed? Are repeats allowed? NO YES NO YES Combination Permutation Decision Chart nPr

22. You go to 31 flavors Ice Cream. Determine the number of ways you can order the following on an ice cream cone.. • a triple scoop (with no repeats) Does order matter? NO YES Are repeats allowed? Are repeats allowed? NO YES NO YES Combination Permutation Decision Chart nPr

23. Finish the assignment: Log Practice and IC 40, 41, 43 – 48