Over Lesson 13–1
Nia and Chad are going to a concert with their high
school’s key club. If they choose a seat on the row
below at random, what is the probability that Chad
will be in seat C11 and Nia will be in C12?
1
132
A.
B.
C.
D.
A
B
C
D
Over Lesson 13–1
A store randomly assigns their employees work
identification numbers to track productivity. Each
number consists of 5 digits ranging from 1-9. If the
digits cannot repeat, find the probability that a
randomly generated number is 25938?
𝟏
𝟏𝟓, 𝟏𝟐𝟎
A.
B.
C.
D.
A
B
C
D
Over Lesson 13–1
What is the probability that a zip code randomly
generated from among the digits 3, 7, 3, 9, 5, 7, 2
and 3 is the number 39372?
𝟏
𝟑𝟑𝟔𝟎
A.
B.
C.
D.
A
B
C
D
• Use circular permutations with probability.
• Use combinations with probability.
Probability and Circular Permutations
A. SEATING If 8 students
sit at random in the circle of
chairs shown, what is the
probability that the students
sit in the arrangement
shown? Explain your
reasoning.
Since there is no fixed reference
point, this is a circular permutation. So there are
(8 – 1)! or 7! distinguishable permutations of the way
the students can sit.
Probability and Circular Permutations
Answer: The probability of the students sitting in the
arrangement shown is
Probability and Circular Permutations
B. CRAYONS You purchase a box of 8 crayons. If
the crayons are packaged in random order, what
is the probability that the crayon on the far left is
red? Explain your reasoning.
Since the crayons are packaged in a row, instead of a
circle with no fixed reference point, this is a linear
permutation. In that case, since there are 8 positions
and 1 red crayon, the probability that the crayon on the
far left is red is
Answer:
A. TABLE SETTINGS If for a
birthday party there are 5 people
having cake, and there are 5
different colored plates, what is the
probability that if chosen at random
the plates will be displayed as seen
in the order at the right?
A.
B.
C.
D.
A
B
C
D
B. CONSTRUCTION A home builder is
constructing 6 different models of homes on a
major cross street, 5 of which are 2-floored homes,
and only 1 home that is 1 floor. If built at random,
what is the possibility the 1-floored home will be
on the 1st plot of land?
A.
B.
C.
D.
A
B
C
D
or
n
Cr 
P (n, r )
r!
Probability and nCr
A set of alphabet magnets are placed in a bag. If
5 magnets are drawn from the bag at random,
what is the probability that they will be the letters
a, e, i, o, and u?
Step 1
Since the order in which the magnets are
chosen does not matter, the number of
possible outcomes in the sample space is
the number of combinations of 26 letters
taken 5 at a time, 26C5.
Probability and nCr
Step 2
There is only one favorable outcome that all
5 letters are a, e, i, o, and u. The order in
which they are chosen is not important.
Step 3
So, the probability of just getting a, e, i, o,
and u is
Answer:
A set of alphabet magnets are placed in a bag. If
4 magnets are drawn from the bag at random, what
is the probability that they will be the letters m, a, t,
and h?
A.
B.
C.
D.
A
B
C
D