Algebra II
Notes 12.1 Continued
Permutations – the number of ways “r” objects can be taken from a group of “n” objects where
the order that you take them matters.
n!
OR
( n − r )!
in your calculator under Type in value for “n” first.
MATH → PRB
2: nPr
Type in value for r.
Recall the formula for Permutations is n Pr =
Ex: There are 12 books on the summer reading list. You want to read some or all of them. In
how many orders can you read:
a.) 4 of the books?
b.) all 12 of the books?
Permutations with Repetitions – all the permutations we have looked at thus far have had all
objects “distinct”. For example, what if you wanted to arrange the letters MOM in all the
possible arrangements? You would have certain “word” arrangements that would appear to be
the same.
MOM
OMM
MMO
MOM
OMM
MMO
But, the 1st and 4th form the same “word”, the 2nd and the 5th are the same, and 3rd and the 6th are
the same.
n!
where n is the number
q1 ! ⋅ q2 !⋅...
of total objects and each q-value would be the number of times an object repeats.
So, for permutations with repetition we can use the formula:
For MOM example: # of permutations or number of “word” arrangements =
3! 3 ⋅ 2 ⋅1
=
=3
2!
2 ⋅1
EX: Find the number of “word” arrangements for each.
A.)
OHIO
B.)
C.)
MATHEMATICS
MISSISSIPPI
D.) Your dog had 8 puppies, 3 male and 5 female. One possible birth order is MMMFFFFF.
How many different birth orders are possible?
Assign p. 705 – 706 #20, 22, 32 – 38 Even, 39 – 53 Odd
Assign p. 706 #40 – 54 Even, 55, 56, 57, 63
Assign Practice Wkst 12.1A