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Step-by-step explanation:
Let, there are ten persons A, B, C, D, E, F, G, H, I and J.
Total possible seating arrangement in the round table = (10–1)! = (9!).
Let, three persons A, B and C want to seat consecutively; so, their clubbing may be treated as a single entity called K.
So, it practically becomes a permutation among D, E, F. G, H, I , J and K in the round table, which can happen in (8 - 1)! = (7!) ways.
Now, for each such above permutation, K itself can be permuted in (3!) ways.
So, the answer will be = (7!)*(3!) = 5040*6 = 30240.