Kate, Demi, Madona, Sharon, Britney and Nicole

There are 120 different possible seating arrangments.
Note that on a round table ABCDEF and BCDEFA is the same.
The first person can sit on any one of the seats. Now, for the second person there are 5 options, for the third person there are 4 options, for the forth person there are 3 options, for the fifth person there are 2 options and for the last person there is just one option.
Thus, total different possible seating arrangements are
= 5 * 4 * 3 * 2 * 1
= 120