Algebra II Honors/Gifted Name___________________________________ @

Period_____Date_________________________

PROBABILITIES OF VARIOUS PERMUTATIONSPROBABILITIES OF VARIOUS PERMUTATIONSHANDOUTHANDOUT

1) Define permutation. __________________________________________________________________

__________________________________________________________________________________________

2) ! means “factorial”. That is 4! = 4 • 3 • 2 • 1. Find

a) 8! ______________________________________________________________________________

b) n! ______________________________________________________________________________

c) (n + 2)! _________________________________________________________________________

3)a) Arrange the letters in the word “rat” in all possible ways. ____________________________

__________________________________________________________________________________________

b) How many different arrangements are there? _______ or ______! This can also be

written using the symbols 3P3, read, “The permutation of three choose three.”

c) Read 7P5 This means we have 7 objects to choose from and we will arrange 5 of

them at a time.

4) Find :a) 8P3 __________ b) 5P4 __________ c) 7P7 __________

5) Ok, we need 5 students to come to the front of the room. Now. What are you waiting for?

a) How many different arrangements are there for these students? __________________

b) If one student must be in the middle, how many different arrangements are there

now? ____________________________________________________________________________c) How many different arrangements are there if the last position must

be held by a

female? __________________________________________________________________________

6) Find all distinguishable permutations of the letters in the word R E V E R S E.

____________________________________________________. Since we can not tell the difference between the e’s and the r’s, the arrangements REVERSE and REVERSE are not distinguishable. Yes, they are different. How? We must account for the fact the two arrangements look alike or are not distinguishable. To find the number of distinguishable permutations for

REVERSE, we use the set-up .

Where does the 2! and 3! come from? ____________________________________________________

_________________________________________________________________________________________

7) Find the number of distinguishable permutations for :

a) SARAHTHOMASSON ___________________________________________________________

b) Mississippi ____________________________________________________________________

c) 43434355343 ____________________________________________________________________

8) Now that we have finished the easy part!, let’s discuss circular permutations …….How many circular permutations could be made from :

a) AEIOU ________________ b) QUADRATIC ___________________