Question 44

Eight members of different ages from the same family sit around a circular table for dinner. In how many ways can they be arranged such that on either side of younger members there are elder members seated?

Solution

From the question, we should arrange younger and older people in an alternate manner.

First, we should arrange the 4 elder people in a circular arrangement in (4 - 1)! = 6 ways.

Now, for the 4 younger people, this is similar to a linear arrangement, as the gaps are distinct positions = 4! = 24 ways.

=> Required number of total arrangements = 6 * 24 = 144 ways.

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