PermutationsAn arrangement of all or part of a number of things in adefinite order.Order of the Arrangement Counts!!!Permutations are used to generate:- license plate numbers- phone numbers- social insurance numbers- locker combinations
We show permutations with the symbol "nPr" which reads the number of permutations of "n" things arranged or taken or picked "r" at a timeFor example,How many 2-letter "words" can be made using the lettersof the alphabet?Two solutions possible
Ex)(a) How many permutations can be formed from theletters in the word JUSTICE using all 7 letters? In general, Pr = n n! n r (n - r)! n NUsing the above example..
(b) How many permutations can be formed from JUSTICE using only 5 letters at a time? or 7P5 says "using 7 objects picking or arranging them 5 at a time" Also reads "7 pick 5" On calculator 7P5 = Or 7P5 =
Ex)A group of 9 different books are to be selected andarranged on a shelf for display.How many arrangements are possible?or9P4 =Note: Arrangement, lineup, selected suggest order or perms.
Using nPr to solve for n or rEx) Solve for n, given nP2 = 30Ex) Solve for r, given 5Pr = 20
Perms with Repeating ObjectsEx) How many ways can you arrange the letters of "WOW"?We can only tell 3 apart.The other 3 are not distinguishable.Since the W repeats twice, we correct by dividing by 2!
Ex) How many ways can you arrange the letters of WOWW? In general, the number of perms of n objects with r identical objects is n! r!Ex) Using all letters in the AARDVARK how many different arrangements are possible?