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Counting principle
A resort manager is choosing a committee of four people to discuss employment issues. They' II choose from eight housekeepers, three desk clerks, and five mai ntenance w orkers. H ow many possible comma ttees are there if there have to be at least two housekeeper
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(Ctrl)
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Tessa is creating a media center. There are
5
5
5
televisions and
2
2
2
sets of speakers to choose from. How many different entertainment centers can Tessa make?
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_
_
_
_
\_\_\_\_
____
entertainment centers
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8
8
8
A test has
30
30
30
questions worth
100
100
100
points. The test consists of true/false questions worth
2
2
2
points and some multiple choice questions worth
12
12
12
points. The number of true/false questions in the test are
□
\square
□
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6
6
6
. Multiple Representations Suppose the data described above for the electronics store were represented with a bar graph instead of a dot plot. Would there be any advantages
0
0
0
disadvantages?
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According to the Project Cash information above, what is the cost to complete this project in the normal time?
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$
40
\$ 40
$40
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$
120
\$ 120
$120
\newline
$
145
\$ 145
$145
\newline
$
405
\$ 405
$405
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A committee must be formed with
3
3
3
teachers and
5
5
5
students. If there are
11
11
11
teachers to choose from, and
12
12
12
students, how many different ways could the committee be made?
\newline
Answer:
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A committee must be formed with
3
3
3
teachers and
3
3
3
students. If there are
8
8
8
teachers to choose from, and
16
16
16
students, how many different ways could the committee be made?
\newline
Answer:
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A committee must be formed with
5
5
5
teachers and
3
3
3
students. If there are
7
7
7
teachers to choose from, and
8
8
8
students, how many different ways could the committee be made?
\newline
Answer:
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A committee must be formed with
4
4
4
teachers and
3
3
3
students. If there are
10
10
10
teachers to choose from, and
16
16
16
students, how many different ways could the committee be made?
\newline
Answer:
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A committee must be formed with
3
3
3
teachers and
7
7
7
students. If there are
9
9
9
teachers to choose from, and
15
15
15
students, how many different ways could the committee be made?
\newline
Answer:
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A committee must be formed with
2
2
2
teachers and
3
3
3
students. If there are
7
7
7
teachers to choose from, and
17
17
17
students, how many different ways could the committee be made?
\newline
Answer:
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A committee must be formed with
3
3
3
teachers and
4
4
4
students. If there are
10
10
10
teachers to choose from, and
13
13
13
students, how many different ways could the committee be made?
\newline
Answer:
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A committee must be formed with
5
5
5
teachers and
5
5
5
students. If there are
9
9
9
teachers to choose from, and
14
14
14
students, how many different ways could the committee be made?
\newline
Answer:
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Sandy makes
$
2
\$ 2
$2
profit on every cup of lemonade that she sells and
$
1
\$ 1
$1
on every cupcake that she sells. Sandy wants to sell at least
5
5
5
cups of lemonade and at least
5
5
5
cupcakes per day. She wants to earn at least
$
25
\$ 25
$25
per day. Show and describe all the possible combinations of lemonade and cupcakes that Sandy needs to sell to meet her goals. List two possible combinations.
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Russell is picking out a new lamp at a furniture store. There are
6
6
6
kinds of lamp bases and
3
3
3
different lampshades. How many different lamps can Russell choose?
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_
_
_
_
\_\_\_\_
____
lamps
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Damon is decorating his bedroom. There are
3
3
3
shades of paint and
5
5
5
styles of furniture to choose from. How many different ways can Damon customize his dorm room?
\newline
_
_
_
_
\_\_\_\_
____
ways
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Alvin thought dressing up as a ghost for Halloween would be simple, but there were still many decisions to make. He has
5
5
5
different colored sheets and can cut
2
2
2
different eyehole shapes. How many different ways can Alvin dress up as a ghost?
\newline
_
_
_
_
\_\_\_\_
____
ways
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Question
25
25
25
,
11
11
11
.
3
3
3
.
44
44
44
\newline
points
\newline
Points:
0
0
0
of
1
1
1
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Solve by the method of your choice.
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Twenty-eight people purchase raffle tickets. Three winning tickets are selected at random. If first prize is
$
5000
\$ 5000
$5000
, second prize is
$
4500
\$ 4500
$4500
, and third prize is
$
500
\$ 500
$500
, in how many different ways can the prizes be awarded?
\newline
There are
□
\square
□
different ways in which the prizes can be awarded.
\newline
(Simplify your answer.)
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