Transcript Chapter 5 Probability - Department of Mathematics and

Chapter 5
Probability
5.5
Counting Techniques
Multiplication Principle of Counting
If a task consists of a sequence of choices in
which there are p selections for the first
choice, q selections for the second choice, r
selections for the third choice, and so on.
Then the task of making these selections
can be done in the following number of
different ways.
If a license plate consists of a letter,
then 5 numbers, how many different
types of license plates are
possible?
If a license plate consists of a letter,
then 5 numbers, how many different
types of license plates are
possible?
Suppose that you have 5 different trees
that you wish to plant. In how many
different ways can the 5 trees be
planted in a row?
A permutation is an ordered
arrangement of n distinct objects
without repetitions. The symbol nPr
represents the number of permutations
of n distinct objects, taken r at a time,
where r < n.
Determine the value of 9P3.
Suppose a committee consists of 10 people.
In how many ways can the chair and vicechair of the committee be chosen if the first
person randomly selected is the chair and
the second person randomly selected is the
vice-chair.
A combination is an arrangement,
without regard to order, of n distinct
objects without repetitions. The symbol
nCr represents the number of
combinations of n distinct objects taken
r at a time, where r < n.
Determine the value of 9C3.
The United States Senate consists of 100
members. In how many ways can 4
members be randomly selected to attend a
luncheon at the White House?
A landscape architect has 3 Sugar Maples,
2 Weeping Willows, and 4 Green Ash trees
to plant along a street in a new
subdivision. In how many different ways
can the trees be planted?
What is the probability of obtaining 3
of a kind when 5 cards are drawn
from a standard 52-card deck?
What is the probability of obtaining 3
of a kind when 5 cards are drawn
from a standard 52-card deck?
P(3 of a kind)
= 0.0211