I see this as arranging 3 people in a row. My answer would be 3!=3x2x1=6

I hope its correct. This is my first post

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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

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
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