[Math] In how many ways can 10 married couples line up for a photograph if every wife stands next to her husband

Question

In how many ways can $10$ married couples line up for a photograph if every wife stands next to her husband?

I've given this a shot, now I just wanna compare my answers to see if I'm correct.

My answer is $2 \times 10!$ , the $2$ is because you can have either the husband standing first then the wife and vise versa. the $10!$ is the ways the arrange each couple.

Answer 1

First, label the couples $1$ through $10$ and choose an order for them in $10!$ ways. Then, for each of the ten couples, choose whether the wife or the husband goes before in $2$ ways, for a total of $2^{10}\cdot10!$ ways.