6 different people chosen from 7 can sit around the circular table in 840 ways.
Given that there are 7 people who have arrived for dinner.
But the circular table only seats 6.
Hence 1 person can be left out.
This can be done in 7 ways, which is a simple case of permutation.
A permutation is a combination of objects arranged in a particular sequence. The elements of sets are arranged in this case in a linear or sequential sequence.
Now 6 people will have to sit on the circular table.
Now from the properties of combination we know that , if n people sit around a circular table, then they can sit in n! ways.
Therefore 6 people can sit around a circular table in 6! ways.
6! = 120
Therefore total number of ways = 120 × 7 = 840
Hence 6 different people chosen from 7 can sit around the circular table in 840 ways.
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