Seven in a Line, Adjacent

Combinatorics
Permutations
Easy
Seven people stand in a line. How many arrangements have two particular people, Alice and Bob, standing adjacent?
Hint 1

Treat Alice and Bob as a single combined block.

Hint 2

Arrange the block together with the other five people, and account for the two internal orders of the block.

Show worked solution
  1. 1. Merge into a block

    Treating Alice and Bob as one unit leaves units to arrange, and the pair can be internally ordered ways.

Answer: 1440

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