6/20/23,q8:26qA AqFirstqCourseqInqProbabilityqSolutionqManu
M al
Solutions Manual q
AqFirstq Courseq in
PROBABILITY SeventhqEdition
Sheldon Ross q
Prenticeq Hall,q Upperq Saddleq Riverq NJq 07458
about:blank 1/148
,6/20/23,q8:26qA AqFirstqCourseqInqProbabilityqSolutionqManu
M al
about:blank 2/148
,6/20/23,q8:26qA AqFirstqCourseqInqProbabilityqSolutionqManu
M al
TableqofqContents
Chapterq1............................................................................. 1
Chapterq2............................................................................. 10
Chapterq3............................................................................. 20
Chapterq4............................................................................. 46
Chapterq5............................................................................. 64
Chapterq6............................................................................. 77
Chapterq7............................................................................. 98
Chapterq8............................................................................. 133
Chapterq9............................................................................. 139
Chapterq10 ........................................................................... 141
about:blank 3/148
, 6/20/23,q8:26qA AqFirstqCourseqInqProbabilityqSolutionqManu
M al
Chapterq1
Problems
1.
(a)qByqtheqgeneralizedqbasicqprincipleqofqcount
ingqthereqareq26q ⋅q26q ⋅q10q ⋅q10q ⋅q10q ⋅q10q ⋅q10 q =q 6
7,600,000
(b)q 26q ⋅q25q ⋅q10q ⋅q9q ⋅q8q ⋅q7q ⋅q6q =q 19,656,000
2. 64q=q1296
3. Anqassignmentqisqaqsequenceqi1,q…,qi20qwhereqijqisqtheqjobqtoqwhichqpersonqjqisqassigned.q
Sinceqonlyqoneqpersonqcanqbeqassignedqtoqaqjob,qitqfollowsqthatqtheqsequenceqisqaqpermuta
tionqofqtheqnumbersq1,q…,q20qandqsoqthereqareq20!qdifferentqpossibleqassignments.
4. Thereqareq4!qpossibleqarrangements.qByqassigningqinstrumentsqtoqJay,qJack,qJohnqandqJim,
qinqthatq order,q weq seeq byq theq generalizedq basicq principleq thatq thereq areq 2q ⋅q1q ⋅q2q ⋅q1q =q 4q p
ossibilities.
5. Thereq wereq 8q ⋅q2q ⋅q9q =q 144q possibleq codes.q Thereq wereq 1q ⋅q2q ⋅q9q =q 18q thatq startedq withq aq 4.
6. Eachqkittenqcanqbeqidentifiedqbyqaqcodeqnumberqi,qj,qk,qlqwhereqeachqofqi,qj,qk,qlqisqanyqo
fqtheqnumbersqfromq1qtoq7.qTheqnumberqiqrepresentsqwhichqwifeqisqcarryingqtheqkitten,qjqt
henqrepresentsqwhichqofqthatqwife’sq7qsacksqcontainqtheqkitten;qkqrepresentsqwhichqofqtheq
7qcatsqinqsackqjqofqwifeqiqisqtheqmotherqofqtheqkitten;qandqlqrepresentsqtheqnumberqofqtheq
kittenqofqcatqkqinqsackq jq ofq wifeq i.q Byq theq generalizedq principleq thereq areq thusq 7q ⋅q7q ⋅q7q ⋅q7
q =q 2401q kittens
7. (a)q6!q=q720
(b)q 2q⋅q3!q⋅q3!q=q72
(c)q 4!3!q=q144
(d)q 6q ⋅q3q ⋅q2q ⋅q2q ⋅q1q ⋅q1q =q 72
8. (a)q5!q=q120
7!
(b) =q1260
2!2!
11! =q34,650
(c)
4!4!2!
7!
(d) =q1260
2!2!
(12)!q
9. =q27,720
6!4!
10. (a)q 8!q=q40,320
(b)q 2q⋅q7!q =q 10,080
(c)q 5!4!q=q2,880
(d)q 4!24q=q384
Chapterq1 1
about:blank 4/148
M al
Solutions Manual q
AqFirstq Courseq in
PROBABILITY SeventhqEdition
Sheldon Ross q
Prenticeq Hall,q Upperq Saddleq Riverq NJq 07458
about:blank 1/148
,6/20/23,q8:26qA AqFirstqCourseqInqProbabilityqSolutionqManu
M al
about:blank 2/148
,6/20/23,q8:26qA AqFirstqCourseqInqProbabilityqSolutionqManu
M al
TableqofqContents
Chapterq1............................................................................. 1
Chapterq2............................................................................. 10
Chapterq3............................................................................. 20
Chapterq4............................................................................. 46
Chapterq5............................................................................. 64
Chapterq6............................................................................. 77
Chapterq7............................................................................. 98
Chapterq8............................................................................. 133
Chapterq9............................................................................. 139
Chapterq10 ........................................................................... 141
about:blank 3/148
, 6/20/23,q8:26qA AqFirstqCourseqInqProbabilityqSolutionqManu
M al
Chapterq1
Problems
1.
(a)qByqtheqgeneralizedqbasicqprincipleqofqcount
ingqthereqareq26q ⋅q26q ⋅q10q ⋅q10q ⋅q10q ⋅q10q ⋅q10 q =q 6
7,600,000
(b)q 26q ⋅q25q ⋅q10q ⋅q9q ⋅q8q ⋅q7q ⋅q6q =q 19,656,000
2. 64q=q1296
3. Anqassignmentqisqaqsequenceqi1,q…,qi20qwhereqijqisqtheqjobqtoqwhichqpersonqjqisqassigned.q
Sinceqonlyqoneqpersonqcanqbeqassignedqtoqaqjob,qitqfollowsqthatqtheqsequenceqisqaqpermuta
tionqofqtheqnumbersq1,q…,q20qandqsoqthereqareq20!qdifferentqpossibleqassignments.
4. Thereqareq4!qpossibleqarrangements.qByqassigningqinstrumentsqtoqJay,qJack,qJohnqandqJim,
qinqthatq order,q weq seeq byq theq generalizedq basicq principleq thatq thereq areq 2q ⋅q1q ⋅q2q ⋅q1q =q 4q p
ossibilities.
5. Thereq wereq 8q ⋅q2q ⋅q9q =q 144q possibleq codes.q Thereq wereq 1q ⋅q2q ⋅q9q =q 18q thatq startedq withq aq 4.
6. Eachqkittenqcanqbeqidentifiedqbyqaqcodeqnumberqi,qj,qk,qlqwhereqeachqofqi,qj,qk,qlqisqanyqo
fqtheqnumbersqfromq1qtoq7.qTheqnumberqiqrepresentsqwhichqwifeqisqcarryingqtheqkitten,qjqt
henqrepresentsqwhichqofqthatqwife’sq7qsacksqcontainqtheqkitten;qkqrepresentsqwhichqofqtheq
7qcatsqinqsackqjqofqwifeqiqisqtheqmotherqofqtheqkitten;qandqlqrepresentsqtheqnumberqofqtheq
kittenqofqcatqkqinqsackq jq ofq wifeq i.q Byq theq generalizedq principleq thereq areq thusq 7q ⋅q7q ⋅q7q ⋅q7
q =q 2401q kittens
7. (a)q6!q=q720
(b)q 2q⋅q3!q⋅q3!q=q72
(c)q 4!3!q=q144
(d)q 6q ⋅q3q ⋅q2q ⋅q2q ⋅q1q ⋅q1q =q 72
8. (a)q5!q=q120
7!
(b) =q1260
2!2!
11! =q34,650
(c)
4!4!2!
7!
(d) =q1260
2!2!
(12)!q
9. =q27,720
6!4!
10. (a)q 8!q=q40,320
(b)q 2q⋅q7!q =q 10,080
(c)q 5!4!q=q2,880
(d)q 4!24q=q384
Chapterq1 1
about:blank 4/148
