If people are seated in a random manner in a row containing seats, what is the probability that no two people will occupy adjacent seats?

My solution:

There are favourable arrangements.

Total no. of arrangements:

The 1st person can sit on any of the seats, the 2nd person can sit on any of the other seats and so on. So, the number of ways to seat people on seats is .

But the answer given in the book is . Where have I gone wrong?