February 28, 2011
Permutations and Combinations
February 28, 2011
February 28, 2011
Suppose you are selecting 2 juniors to be
president and vice-president. If Sam, Joe,
and Matt are the candidates, how many
possible president and vice-president
combinations are there?
Suppose you are selecting 2 juniors
to represent the class. If Sam, Joe, and
Matt are the candidates, how many possible
combinations are there?
February 28, 2011
Suppose you are selecting 2 juniors
to represent the class. If Sam, Joe, and
Matt are the candidates, how many possible
combinations are there?
February 28, 2011
The number of permutations of n
distinct objects selected k at a time
is
The number of combinations of n
objects chosen k at a time is
February 28, 2011
1.A group of 9 people are invited to play
a trivia game. Six are selected for the
first round. How many ways could the
first group be selected?
2. At a high school there are two
administrators and three counselors
who park in the three reserved
(numbered) places. In how many ways
could these spaces be occupied by the
cars belonging to these people?
February 28, 2011
3. A six-letter permutation is selected
at random from the letters in the
word FROSTY.
a. How many permutations are possible?
b. How many permutations begin with a T?
c. What is the probability that the
permutation begins with a T?
February 28, 2011
4. A pizza parlor has eleven different
kinds of toppings they can put on their
pizza. How many different kinds of
pizza could they make using
a. three of the toppings?
b. five of the toppings?
c. three or five of the toppings?
February 28, 2011
5. In how many distinguishable ways can
the letters in BANANA be written?
6. In a certain state the automobile
license plates consist of two letters
followed by four digits. How
many distinct plates can be formed?
February 28, 2011
7. Six boys try out for the four positions
on the varisty soccer team.
a. In how many ways could the positions
be filled if there are no restrictions
on who plays which position?
b. In how many ways could the positions
be filled if Mike must be the goalie?
c. If the positions are selected at
random, what is the probability that
Mike will be goalie?
February 28, 2011
7.
a group
of six women
and four
8. AFrom
5-letter
permutation
is selected
at men,
five willfrom
be selected
to serve
on aWhat
random
the letters
GRATE.
Howthat
many committees can be
iscommittee.
the probability
formed with
a. The second letter is T and the last
a. letter
3 men is
and
G?2 women?
b.
b.
c.
2 men and 3 women?
The second letter is a vowel and the
third
a consonant?
Nick, is
one
of the men?
c. The second and third letters are both
consonants?
d. The secod letter is a consonant and the
last letter is E?
February 28, 2011
9. How many different circular
permutations could be made from
ABCD?
February 28, 2011
10. Kay Paso, who is three years old,
tears the labels off all 10 of the
soup cans on her mother's shelf. Her
mother knows that there were 2 cans of
tomato soup and 8 cans of vegetable.
She selects 4 cans at random.
a. What is the probability that exactly 1
of the 4 cans is tomato?
b. What is the probability that at least 1
of the 4 cans is tomato?
c. What is the probability that none of the
4 cans is tomato?
February 28, 2011
11. In how many was could King Arthur's
twelve knights be seated around the
Round Table?
February 28, 2011
12. The varsity croquet team, 4 boys and 8
girls, travels to an out-of-town game.
Their coach will take 7 of them in her
station wagon. If they get into cars at
random, what is the probability that
the coach's car has
a. 2 boys and 5 girls?
b. all girls?
c. all boys?
d. Peter, one of the boys?
February 28, 2011
HW: p.646 #1-19 odd and p.658 #17-35 odd