How this calculation works
For total 5 split into two parts, 1+4 and 4+1 are separate compositions.
THE FORMULA
C(total − 1, parts − 1)A worked example
Split seven unit marks at two of the six interior gaps to get 15 compositions.
Good to know
A composition has no zero parts.
Reference: NIST DLMF, Functions of Number Theory (opens in a new tab) ↗
Read the result
Count ordered ways to split a positive total into a fixed number of positive parts.
The primary result is labeled “Compositions”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
A composition has no zero parts.
For a related exercise, try the greatest common divisor.
A few questions, answered
How can I check the default inputs by hand?
Split seven unit marks at two of the six interior gaps to get 15 compositions.
Which rule does this calculator apply?
C(total − 1, parts − 1)