How this calculation works
If each box must receive at least one item, assign those items first and use the remaining items in the nonnegative allocation.
THE FORMULA
C(items + boxes − 1, boxes − 1)A worked example
Seven items into four labeled boxes yield C(10,3) = 120 allocations.
Good to know
Empty boxes are allowed.
Reference: NIST DLMF, Functions of Number Theory (opens in a new tab) ↗
Read the result
Count nonnegative allocations of identical items to distinct boxes.
The primary result is labeled “Distributions”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Empty boxes are allowed.
For a related exercise, try the greatest common divisor.
A few questions, answered
How can I check the default inputs by hand?
Seven items into four labeled boxes yield C(10,3) = 120 allocations.
Which rule does this calculator apply?
C(items + boxes − 1, boxes − 1)