April 08, 2016
Obj: To use permutations and combinations with probability.
Distinguishable Permutations:
If an n-set contains n1 objects of a first kind, n2 objects of
a second kind, and so on, with n1 + n2 + ... nk = n, then the number of
distinguishable permutations of the n-set is :
n!
n 1!n !n2 !...n3!
k
How many distinguishable permutations are in the letters below?
M
I
S
S
I
S
S
I
P
P
I
April 08, 2016
Obj: To use permutations and combinations with probability.
Find the number of ways one can choose two marbles from
a bag containing three marbles:
1. if the order is important
2. if the order is not important
April 08, 2016
Obj: To use permutations and combinations with probability.
Permutations: order matters
Combinations: order does NOT matter
n!
(n-r)!
nPr =
n
C
r
=
n!
r!(n-r)!
April 08, 2016
Obj: To use permutations and combinations with probability.
Combination Counting Formula:
The number of combinations of n objects taken r at a time is
denoted:
n
C
r
=
n!
r!(n-r)!
April 08, 2016
Obj: To use permutations and combinations with probability.
Permutation or Combination? Then determine the result.
a. A president, vice president, and secretary are chosen from a 25-member club.
b. A cook chooses 5 potatoes from a bag of 12 potatoes to make potato salad.
c. A teacher makes a seating chart for 22 students in a class with 30 desks.
d. Selecting the starting 5 players from a team of 12 basketball players.
April 08, 2016
Obj: To use permutations and combinations with probability.
Recall:
Probability of an Event =
# favorable outcomes
# of total possible outcomes
Ex. What is the probability of rolling a 1 or a 5 on a six-sided die?
P(1 or 5) =
April 08, 2016
Obj: To use permutations and combinations with probability.
Example: (Puppies)
There are 12 puppies for sale at the local pet shop. 4 are brown, 4 are black, 3
are spotted, and 1 is white. What is the probability that if four puppies are
sold, they will all be the brown puppies?
April 08, 2016
Obj: To use permutations and combinations with probability.
Example: (Talent Show)
Chris and Mia, along with 18 other people, sign up to audition for a talent
show. Contestants are called at random to perform for the judges. What is
the probability that Chris will called to perform first and Mia will be called
second?
April 08, 2016
April 08, 2016
Obj: To use permutations and combinations with probability.
HF:
(HR) (13.2)Pg.927: 6-17a,b