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  • A music band consists of 10 members. In how many different ways can they be seated around a circular table if two specific members always sit together?

A music band consists of 10 members. In how many different ways can they be seated around a circular table if two specific members always sit together?

Option: 1

28540


Option: 2

32680


Option: 3

40320


Option: 4

54140


Answers (1)

best_answer

If two specific members always sit together, we can treat them as a single entity. This means we have 9 entities to arrange around the circular table.

The number of ways to arrange 9 entities around a circular table is given by,

(9-1)!=8!

However, since the two specific members within the group can be arranged among themselves in 2! = 2  ways, we need to multiply the result by 2.

Therefore, the total number of different ways the band members can be seated around the circular table, considering the two members sitting together, is

8! \times 2 =40320

Hence, there are 40,320 different ways the band members can be seated around the circular table while ensuring that the two specific members always sit together.

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