2. There are 3 horses (labeled A, B and C) racing for different places. Draw tree diagram to show 1. In how many ways can the horses be placed as 1 st, 2 nd and 3rd? 2. In how many ways can the horses be placed as 1 st and 2 nd ? Aim: What are the permutation and combination? Do Now: 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 We denote it as 3 P 3 which is the same as 3! A permutation is an arrangement of objects in a specific order. #2 3 · 2 = 6 Besides tree diagram, we can use permutation To find the answer We denote it as 3 P 2 #1 3 · 2 · 1 = 6 can also be done by permutation

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 sells different flavors of ice cream, there are 3 chocolates, 4 vanilla and 5 mangos. In how many ways can 2 chocolates, 1 vanilla and 3 mangos be selected?

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 1 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?