Day 3 examples
- 1. Permutations An arrangement of all or part of a number of things in a definite order. Order of the Arrangement Counts!!! Permutations are used to generate: - license plate numbers - phone numbers - social insurance numbers - locker combinations
- 2. We show permutations with the symbol "nPr" which reads the number of permutations of "n" things arranged or taken or picked "r" at a time For example, How many 2-letter "words" can be made using the letters of the alphabet? Two solutions possible
- 3. Ex) (a) How many permutations can be formed from the letters in the word JUSTICE using all 7 letters? In general, Pr = n n! n r (n - r)! n N Using the above example..
- 4. (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 =
- 5. Ex) A group of 9 different books are to be selected and arranged on a shelf for display. How many arrangements are possible? or 9P4 = Note: Arrangement, lineup, selected suggest order or perms.
- 6. Using nPr to solve for n or r Ex) Solve for n, given nP2 = 30 Ex) Solve for r, given 5Pr = 20
- 7. Perms with Repeating Objects Ex) 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!
- 8. 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?