A seating arrangement is a permutation with a geometric convention and, sometimes, a restriction. Treating a required adjacent pair as one block makes that restriction visible.
Use it for line or circle seatings with the calculator’s single specified two-person rule.
The relationship
The counting rule
together in a line: 2(n−1)!
See the structure
A required pair becomes one movable block
[A B] C D E4 units2 internal orders2 × 4! = 48
Worked example
Check the rule with a small case
Five people in a line with A and B together: 2 × 4! = 48.
Interpret with care
Choose the right counting model
More complex adjacency, separation, or named-seat restrictions are not inferred by this focused tool.
Choose a line or circle and an optional two-person restriction.
Read the exact arrangement count.
Calculation method
Use blocks for adjacent people
Unrestricted line and circle counts are n! and (n−1)!. Treating two specified people as a two-order block counts adjacent arrangements; subtracting that count gives non-adjacent arrangements.
Worked example
Five people in a line with two together
Treat the specified pair as one block, arrange four units, then order the pair two ways.
2×4! = 48
Supported inputs
Precision and limits
Discrete domain
Inputs are whole counts. Negative, fractional, grouped, and scientific-notation inputs are rejected.
Exact integers
Results use arbitrary-precision integers and are never rounded. Inputs and output size are bounded to keep the page responsive.
Restriction scope
The restricted modes apply to exactly two specified distinct people. More complex adjacency rules are not inferred.
