How this calculation works
Count ways to partition labeled items into unordered blocks with an internal order in each block.
THE FORMULA
L(n,k)=C(n−1,k−1)n!/k!A worked example
Four items into two lists give C(3,1) × 4!/2! = 36.
Good to know
Order within a block matters. Block order does not.
Reference: NIST DLMF, Functions of Number Theory (opens in a new tab) ↗
Read the result
Count ways to partition labeled items into unordered blocks with an internal order in each block.
The primary result is labeled “Partitions into lists”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Order within a block matters. Block order does not.
For a related exercise, try the greatest common divisor.
A few questions, answered
How can I check the default inputs by hand?
Four items into two lists give C(3,1) × 4!/2! = 36.
Which rule does this calculator apply?
L(n,k)=C(n−1,k−1)n!/k!