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

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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48
8 ways each group can be arranged internally & there are such 6 combination of couples possible.
.•. 6×8=48

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D. 48

Since as group arrangements are 6 x couple arrangement within themselves 2x2x2

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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