Five people are to be arranged in a row for a group photograph. How many arrangements are there if a married couple in the group insist on sitting next to each other?
A
48
B
24
C
20
D
10
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Treat the couple as one block, giving us 4 units to arrange (the couple + 3 others).
Arrange the 4 units: 4! = 4 x 3 x 2 x 1 = 24.
Arrange the couple within their block: 2! = 2 x 1 = 2.
Total arrangements: 4! \times 2! = 24 \times 2 = 24 \times 2 = 48.
Thus, the total number of arrangements is 48.
Source: Myschool Past Questions Archive (Record #31365)