Respuesta :
240 people can seat in a row without restriction in an arrangement.
A permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set.
Permutations differ from combinations, which are selections of some members of a set regardless of order. For example, written as tuples, there are six permutations of the set {1, 2, 3}, namely (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). These are all the possible orderings of this three-element set. Anagrams of words whose letters are different are also permutations: the letters are already ordered in the original word, and the anagram is a reordering of the letters. The study of permutations of finite sets is an important topic in the fields of combinatorics and group theory.
According to the question:
Consider A and B being the people sitting next to each other, as one entity AB or BA.
There are now 5 entities (one of two persons A and B and five of one single person) that have to be placed in a row.
With AB, there are thus 5! possibilities. With BA, there are also 6! possibilities.
Considering both, there are thus 2× 5! = 240 ways to seat 6 people in a row of six seats if two people insist on sitting next to each other.
Learn more about Arrangement:
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