Question

In how many ways can the team members to be arranged for the temperature in all the mails are always together

Answer 1

Question: 1212 guests at a dinner party are to be seated along a circular table. Suppose that the master and mistress of the house have fixed seats opposite to one another. There are two specified guests who must always be placed next to one another. What is the number of ways in which the company can be placed?

My Method:
Let us first seat the 1212 guests. 22 guests are always beside each other hence considering 1111 guests, the no. of combinations possible are 11!11!. But the 22 people can be arranged in 22 ways, so total no. of combinations is given by 2∗11!2∗11!.
Now the master can be seated between any 22 people except the pair to be seated together. Hence, the no. of possibilities to seat him becomes 1111. The mistress is always opposite to him hence she would not contribute to the no. of total ways.

This gives,
The total no. of ways =2∗11∗11!=2∗11∗11!

The Answer given:
First we seat the 22 specified people in 2∗102∗10 ways and the remaining 1010 people can be arranged in 10!10!ways. So total no. of ways =2∗10∗10!=2∗10∗10!

But I don't understand what does the answer state and how my way is wrong. Can anybody help me understand this...