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Aim: What are the permutation and combination?

Aim: What are the permutation and combination?. Do Now:. 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?.

cynthia-strong
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Aim: What are the permutation and combination?

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  1. Aim: What are the permutation and combination? Do Now: • 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? 2.If four students are scheduled to give a report in class, in how many ways can the students give the report? HW: p.685 # 26,28,45,46,47,49,50,52,53

  2. #1. 4 · 3 =12 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 = 24 This is a permutation We denote it as 4P4 which is the same as 4! nPn = n! = n(n – 1)(n – 2)· ··· · 3 · 2 · 1 A permutation is an arrangement of objects in a specific order.

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

  4. 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.

  5. A combination is an arrangement that the order does not matter. nCr 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?

  6. 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?

  7. 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?

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