Section 6-7 Permutations and Combinations

Permutation Permutation – is an arrangement of items in a particular order.

Permutation Permutation – is an arrangement of items in a particular order. The letters N, O, and W can be arranged in six permutations. 3! = 3*2*1 = 6

Permutation Permutation – is an arrangement of items in a particular order. The letters N, O, and W can be arranged in six permutations. 3! = 3*2*1 = 6 Ex: In how many different orders can ten dogs line up to be groomed?

Permutation Permutation – is an arrangement of items in a particular order. The letters N, O, and W can be arranged in six permutations. 3! = 3*2*1 = 6 Ex: In how many different orders can ten dogs line up to be groomed? 1st way – 10! = 10*9*8*7*6*5*4*3*2*1 = 3,628,800 2nd way – nPr n= # to start r = # of slots 10P10 = 3,628,800

Example Ex – Seven Bands are entered in a contest. First, second, and third places will be given to the top three bands. How many arrangements of first, second and third place are possible within 7 bands?

Example Ex – Seven Bands are entered in a contest. First, second, and third places will be given to the top three bands. How many arrangements of first, second and third place are possible within 7 bands? Answer: 7 P 3

Permutations With Repetition *REGENT QUESTION* Find the number of arrangements of letters that can be formed from the letters of the given word using all letters in each arrangement: 1.TREE

Permutations with Repetition In general the number of permutations of “n” things taken “n” at a time when “r” are identical is N! R!

Permutations With Repetition *REGENT QUESTION* Find the number of arrangements of letters that can be formed from the letters of the given word using all letters in each arrangement: 1.TREE 4! 2!

Permutations with Repetition In general the number of permutations of “n” things taken “n” at a time when “r” are identical is N! R! Try: Mississippi

Permutations with Repetition In general the number of permutations of “n” things taken “n” at a time when “r” are identical is N! R! Try: Mississippi 11! 4!4!2!

Combination Is when order is not important nCr # of objects to be selected # of objects eligible

Example 12C3 = A reading list for a course in world literature has 20 books on it. How many ways are there to choose 4 books to read?

Example 12C3 = A reading list for a course in world literature has 20 books on it. How many ways are there to choose 4 books to read? Answer 20 C 4

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