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In how many ways can a group of 10 persons arrange themselves around a circular table if 3 of them insist on sitting beside each other? *​

Sagot :

Taekimchipeachyggukidn

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.