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Full-length FE mock with insightful analytics, weakness diagnosis, and video explanations!
03 Jan 2017, 23:10
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
56% (00:49) correct
44%
(00:51)
wrong
based on 430
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Three couples need to arranged in a row for a group photo. If the couples cannot be separated, how many different arrangements are possible?
A. 6
B. 12
C. 24
D. 48
E. 96
A. 6
B. 12
C. 24
D. 48
E. 96
04 Jan 2017, 07:24
Kudos
Bookmarks
Six spots to fill. Restriction = No couple should be separated
First spot has 6 choices
Second spot has only 1
Third spot = 4 choices
Fourth spot = 1
Fifth spot = 2
Sixth spot = 1
Thus total arrangements = 6 * 4 * 2 = 48
First spot has 6 choices
Second spot has only 1
Third spot = 4 choices
Fourth spot = 1
Fifth spot = 2
Sixth spot = 1
Thus total arrangements = 6 * 4 * 2 = 48
06 Jan 2017, 11:03
Kudos
Bookmarks
Bunuel
Three couples need to arranged in a row for a group photo. If the couples cannot be separated, how many different arrangements are possible?
A. 6
B. 12
C. 24
D. 48
E. 96
A. 6
B. 12
C. 24
D. 48
E. 96
We need to determine in how many ways three couples can be arranged when each couple must stay together.
We can arrange the three couples as follows:
[A-B], [C-D], [E-F].
(Note: Since each couple must remain together, we have expressed each couple in a bracket.)
Since we have 3 brackets, we can arrange those 3 brackets in 3! or 6 ways. However, we must account for the individual arrangements of each couple, i.e., the number of arrangements within each individual bracket.
Couple AB can be arranged in 2! or 2 ways, couple CD can be arranged in 2! or 2 ways, and couple EF can be arranged in 2! or 2 ways.
Thus, the couples can be arranged in 6 x 2 x 2 x 2 = 48 ways.
Answer: D
