Answer
1260 ways
Work Step by Step
Number of ways in which we can select 4 people out of 10 = 10C6 = 210.
Number of ways in which we can arrange 4 people in a circular table = 4!/4 (because we can only arrange 3 people out of 4, as the 4th person will be determined by the positions of the other 3)
Ways to seat 4 out of 10 people around a circular table = 210$\times$(4!/4) =1260
