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Title: Discrete Math
Description: Are you having issues with your Discrete Math course? Well, here's the first week's test answers.
Description: Are you having issues with your Discrete Math course? Well, here's the first week's test answers.
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Assignment Print View
Score:
1
...
14
%
Award: 2 out of 2
...
How many different types of this shirt are made?
72
If there are n1 ways to do the first task and for each of these ways of doing the first task, there are
n2 ways to do the second task, then there are n1n2 ways to do the procedure
...
References
Section Break
http://ezto
...
com/hm
...
4/8/16, 2:58 AM
Award: 2 out of 2
...
If there are n1 ways to do the first task and for each of these ways of doing the first task, there are
n2 ways to do the second task, then there are n1n2 ways to do the procedure
...
http://ezto
...
com/hm
...
4/8/16, 2:58 AM
Award: 2 out of 2
...
If there are n1 ways to do the first task and for each of these ways of doing the first task, there are
n2 ways to do the second task, then there are n1n2 ways to do the procedure
...
http://ezto
...
com/hm
...
References
Section Break
4
...
00 points
Ch 06 Sec 1 Ex 32 1st
Which rule must be used to find the number of strings of eight uppercase English letters that are
there if the letters can be repeated?
The sum rule
The subtraction rule
The division rule
The product rule
By using the rule the number of strings of eight uppercase English letters that are there if the letters
can be repeated is 268 = 208,827,064,576 strings
...
mheducation
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Page 4 of 30
Assignment Print View
5
...
00 points
Ch 06 Sec 1 Ex 32 2nd
How many strings of eight uppercase English letters are there if no letter can be repeated?
62990928000
If there are n1 ways to do the first task and for each of these ways of doing the first task, there are
n2 ways to do the second task, then there are n1n2 ways to do the procedure
...
mheducation
...
tpx?todo=printview
Page 5 of 30
Assignment Print View
6
...
00 points
Ch 06 Sec 1 Ex 32 3rd
Which rule must be used to find the number of strings of eight uppercase English letters that start
with X, if letters can be repeated?
The subtraction rule
The sum rule
The product rule
The division rule
By using the rule, there are 267 = 8,031,810,176 strings
...
mheducation
...
tpx?todo=printview
Page 6 of 30
Assignment Print View
7
...
00 points
Ch 06 Sec 1 Ex 32 4th
How many strings of eight uppercase English letters are there that start with X, if no letter can be
repeated?
2422728000
If there are n1 ways to do the first task and for each of these ways of doing the first task, there are
n2 ways to do the second task, then there are n1n2 ways to do the procedure
...
mheducation
...
tpx?todo=printview
Page 7 of 30
Assignment Print View
8
...
00 points
Ch 06 Sec 1 Ex 32 5th
Which rule must be used to find the number of strings of eight uppercase English letters that start
and end with X, if letters can be repeated?
The division rule
The sum rule
The subtraction rule
The product rule
By using the rule, there are 266 = 308,915,776 number of strings
...
mheducation
...
tpx?todo=printview
Page 8 of 30
Assignment Print View
9
...
00 points
Ch 06 Sec 1 Ex 32 6th
How many strings of eight uppercase English letters are there that start with the letters BO (in that
order), if letters can be repeated?
308915776
If there are n1 ways to do the first task and for each of these ways of doing the first task, there are
n2 ways to do the second task, then there are n1n2 ways to do the procedure
...
mheducation
...
tpx?todo=printview
Page 9 of 30
Assignment Print View
10
...
00 points
Ch 06 Sec 1 Ex 32 7th
Which rule must be used to find the number of strings of eight uppercase English letters that start
and end with the letters BO (in that order), if letters can be repeated?
The product rule
The subtraction rule
The division rule
The sum rule
By using the rule, there are 264 = 456,976 number of strings for this case
...
mheducation
...
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Page 10 of 30
Assignment Print View
11
...
00 points
Ch 06 Sec 1 Ex 32 8th
The _____ principle is used to find the number of strings of eight uppercase English letters that
start or end with the letters BO (in that order), if letters can be repeated
...
Therefore by the principle,
the are 266+266−264 = 617,374,576 strings
...
mheducation
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Page 11 of 30
Assignment Print View
12
...
00 points
Ch 06 Sec 3 Ex 08
In how many different orders can five runners finish a race if no ties are allowed?
120
The number of different orders is estimated by calculating the value of P(5, 5)
...
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Ch 06 Sec 3 Ex 20
MAIN
Page 12 of 30
Assignment Print View
13
...
00 points
Ch 06 Sec 3 Ex 20 1st
a) exactly three 0s?
120
There are C(10, 3) ways to choose the positions for the 0’s
...
Ch 06 Sec 3 Ex 20
1st
Award: 2 out of 2
...
References
Numeric
Response
Ch 06 Sec 3 Ex 20
2nd
http://ezto
...
com/hm
...
4/8/16, 2:58 AM
Award: 2 out of 2
...
References
Numeric
Response
16
...
00 points
Ch 06 Sec 3 Ex 20 4th
d) at least three 1s?
968
If a string does not have at least three 1’s, then it has 0, 1, or 2 1’s
...
There are 1024 strings in all
...
mheducation
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Page 14 of 30
Assignment Print View
4/8/16, 2:58 AM
Ch 06 Sec 3 Ex 27 MAIN
A club has 25 members
...
Ch 06 Sec 3 Ex 27
MAIN
Award: 2 out of 2
...
References
Numeric
Response
Ch 06 Sec 3 Ex 27
1st
http://ezto
...
com/hm
...
4/8/16, 2:58 AM
Award: 2 out of 2
...
References
Numeric
Response
Ch 06 Sec 3 Ex 27
2nd
Ch 06 Sec 3 Ex 30 MAIN
Seven women and nine men are on the faculty in the mathematics department at a school
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Ch 06 Sec 3 Ex 30
MAIN
Page 16 of 30
Assignment Print View
19
...
00 points
Ch 06 sec 3 Ex 30 1st
a) How many ways are there to select a committee of five members of the department if at least one
woman must be on the committee?
4242
There are C(16, 5) ways to select a committee if there are no restrictions and there are C(9, 5) ways
to select a committee from just the 9 men
...
Ch 06 sec 3 Ex 30
1st
Award: 2 out of 2
...
References
Numeric
Response
Ch 06 Sec 3 Ex 30
2nd
http://ezto
...
com/hm
...
4/8/16, 2:58 AM
Award: 2 out of 2
...
1287
The coefficient of x5y8 is
...
Ch 06 Sec 4 Ex 04
Award: 2 out of 2
...
References
Numeric
Response
Ch 06 Sec 4 Ex 06
http://ezto
...
com/hm
...
4/8/16, 2:58 AM
Award: 2 out of 2
...
References
Numeric
Response
Ch 06 Sec 5 Ex 01
http://ezto
...
com/hm
...
4/8/16, 2:58 AM
Award: 2 out of 2
...
References
Numeric
Response
Chapter: 06
Counting
Ch 06 Sec 5
Ex 05
Section: 06
...
mheducation
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Ch 06 Sec 5 Ex 15
MAIN
Page 20 of 30
Assignment Print View
25
...
00 points
Ch 06 Sec 5 Ex 15 1st
a) x1 ≥ 1?
10626
Let
; thus
is the value that
has in excess of its required 1
...
References
Numeric
Response
26
...
00 points
Ch 06 Sec 5 Ex 15 2nd
b)
for i = 1, 2, 3, 4, 5?
1365
Substitute
into the equation for each i; thus is the value that has in excess of its
required 2
...
References
Numeric
Response
Ch 06 Sec 5 Ex 15
2nd
http://ezto
...
com/hm
...
4/8/16, 2:58 AM
Award: 2 out of 2
...
The
restriction on
will be violated if
11
...
References
Numeric
Response
Ch 06 Sec 5 Ex 15
3rd
http://ezto
...
com/hm
...
4/8/16, 2:58 AM
Award: 2 out of 2
...
Then the problem is equivalent to counting the
, where
, subject to
the constraints that
and
...
Thus if the number of solutions is counted to
, subtract
the number of its solutions in which
, and subtract the numbers of its solutions in which
,to arrive at the answer
...
Applying the first restriction reduces the equation to
, which
has C(5 + 1 − 1, 1) = C(5, 1) = 5 solutions
...
References
Numeric
Response
Ch 06 Sec 5 Ex 15
4th
http://ezto
...
com/hm
...
4/8/16, 2:58 AM
Award: 2 out of 2
...
References
Numeric
Response
Ch 06 Sec 5
Ex 21
30
...
05
Generalized
Permutations and
Combinations
Award: 2 out of 2
...
Since MISSISSIPPI has 4 indistinguishable objects of type S, 4 indistinguishable objects of
type I, and 2 indistinguishable objects of type M, it has
= 831,600strings
...
mheducation
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tpx?todo=printview
= 34,650 strings
...
Preview
Design
Code
References
Multiple
Choice
Chapter: 06
Counting
Ch 06 Sec 5
Ex 30
Section: 06
...
mheducation
...
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Page 25 of 30
Assignment Print View
31
...
00 points
Ch 07 Sec 1 Ex 10
What is the probability that a five-card poker hand contains the two of diamonds and the three of
spades?
(Note: Enter the value in decimal format and report it to four decimal places
...
0075
Compute the number of poker hands that contain the two of diamonds and the three of spades
...
To form the rest of the hand, choose 3 cards
from the 50 remaining cards, so there are C(50, 3) hands containing these two specific cards
...
mheducation
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Page 26 of 30
Assignment Print View
32
...
00 points
Ch 07 Sec 1 Ex 21
What is the probability that a fair die never comes up an even number when it is rolled six times?
(Note: Enter the value of probability in decimal format and round it to three decimal places
...
016
There are 2 equally likely outcomes for the parity on the roll of a die—even and odd
...
References
Numeric
Response
Ch 07 Sec 1 Ex 21
http://ezto
...
com/hm
...
4/8/16, 2:58 AM
Award: 2 out of 2
...
(Note: Enter the value in decimal format and round it to two decimal places
...
35
If the numbers are chosen from the integers from 1 to n, then there are C(n, 6) possible entries
...
Therefore, since the winning numbers are picked at random, the
...
mheducation
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Ch 07 Sec 1 Ex 34
MAIN
Page 28 of 30
Assignment Print View
34
...
00 points
Ch 07 Sec 1 Ex 34 1st
a) no one can win more than one prize
...
References
Multiple
Choice
Chapter: 07 Discrete
Probability
Ch 07 Sec 1
Ex 34 1st
Section: 07
...
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Page 29 of 30
Assignment Print View
35
...
00 points
Ch 07 Sec 1 Ex 34 2nd
b) winning more than one prize is allowed
...
References
Multiple
Choice
Chapter: 07 Discrete
Probability
Ch 07 Sec 1
Ex 34 2nd
Section: 07
...
mheducation
...
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Page 30 of 30
Title: Discrete Math
Description: Are you having issues with your Discrete Math course? Well, here's the first week's test answers.
Description: Are you having issues with your Discrete Math course? Well, here's the first week's test answers.