Question

In how many ways seven people can be arranged in a row? How many of these arrangements can be made if two particular people are never together?​

Answer 1

Answer:

E.g. there are 7 options for the first seat, 6 for the second (because one has been used), 5 for the third, 4 for the fourth, and so on. So there are 5040 ways of arranging seven people in a row of seven chairs.

Step-by-step explanation:

Answer 2

Answer:

Suppose the 2 people are together - you are to arrange 6 ‘units’ around the table. This can be done in [6 - 1]! = 120 ways. As the two person A and B can be arranged as AB or BA, total number of arrangements with the two persons next to each other is 2 x 120 = 240 ways.

7 people can be arrange around a circular table in 6! = 720 ways

So number of arrangement with the 2 persons NOT next to each other is 720 - 240 = 480

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