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Difficulty:
25%
(medium)
Question Stats:
76% (01:39) correct
24%
(02:07)
wrong
based on 852
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In how many ways can 5 identical blue marbles and 6 identical green marbles be arranged in a row such that all the blue marbles are grouped together?
A. 120
B. 30
C. 24
D. 11
E. 7
M04-14
A. 120
B. 30
C. 24
D. 11
E. 7
M04-14
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17 Jun 2015, 02:39
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In how many ways can 5 identical blue marbles and 6 identical green marbles be arranged in a row such that all the blue marbles are grouped together?
A. 120
B. 30
C. 24
D. 11
E. 7
Consider all 5 blue marbles as a single unit: {bbbbb}. Along with the 6 green marbles, we have a total of 7 units: {bbbbb}, {g}, {g}, {g}, {g}, {g}, {g}. The number of arrangements for these 7 units will be 7!/6! = 7.
Answer: E.
A. 120
B. 30
C. 24
D. 11
E. 7
Consider all 5 blue marbles as a single unit: {bbbbb}. Along with the 6 green marbles, we have a total of 7 units: {bbbbb}, {g}, {g}, {g}, {g}, {g}, {g}. The number of arrangements for these 7 units will be 7!/6! = 7.
Answer: E.
General Discussion
23 Apr 2026, 11:30
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Bookmarks
6 identical green marbles can be arranged in a row in one way creating 7 gaps ,
now in each of these gaps all the 5 blue marbles can be placed to satisfy the condition.
hence 7 ways
E
now in each of these gaps all the 5 blue marbles can be placed to satisfy the condition.
hence 7 ways
E
