2. Aim: What are the permutation and combination? Do Now: 2. If four students are scheduled to give a report in class, in how many ways can the students give the report? 1.There are 4 ways from NYC to Albany and 3 ways from Albany to Buffalo. In how many way can Bob select if he is going to Buffalo by way of Albany from NYC? HW: p.685 # 26,28,45,46,47,49,50,52,53

3. n P n = n! = n(n – 1)(n – 2)· ··· · 3 · 2 · 1 The counting Principal: If one activity can occur in any of m ways and a second activity can occur in any of n ways, then both activities can occur in the order given in m · n ways. #2. 4 · 3 · 2 · 1 = 24This is a permutation We denote it as 4 P 4 which is the same as 4! #1. 4 · 3 =12 A permutation is an arrangement of objects in a specific order.

4. n P r is a permutation of n things taken r at a time.,where r is less than n If there are n objects taken n at a time, the permutation is denoted n P n For example: The Math Club has 20 members: In how many ways are there of selecting a president, vice president and secretary?

5. Permutations with repetition In general, the number of permutations of n things taken n at a time when a are identical is: In how many ways can 9 – letter words be formed from the word “CLASSROOM”? S repeated 2 times and O repeated 2 times.

6. A combination is an arrangement that the order does not matter. n C r is a combination of n things taken r at a time. There is another notation for combination For example: The Math Club has 20 members: How many committees of 3 members can be selected?

7. How many different arrangement of 5 letters can be drawn from the alphabet if 3 are consonants and 2 are vowels? A local convenient store hires three students to work. Next month, there are 20 days on which they will work. Alex will work 8 days, Rosa will work 6 days and Carla will work 6 days. In how many ways can their schedule for the month be arranged?

8. 1.In how many different orders can the program for a music recital be arranged if 7 students are to perform? 2. In how many ways can 2 junior and 1 senior be selected from a group of 8 juniors and 6 seniors? 3. A reading list gives the titles of 20 novels and 12 biographies from which each students is to choose 3 novels and 2 biographies to read. How many different combinations of titles can be chosen?