How this calculation works
Choose positions for the first group, then choose positions for the second from those remaining. The third group fills the rest.
THE FORMULA
(a+b+c)! / (a! b! c!)A worked example
Two A, three B and one C can be arranged in 60 distinct orders.
Good to know
Items within each group are indistinguishable.
Reference: NIST DLMF, Functions of Number Theory (opens in a new tab) ↗
Read the result
Count distinct strings with three groups of identical items.
The primary result is labeled “Distinct arrangements”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Items within each group are indistinguishable.
For a related exercise, try the greatest common divisor.
A few questions, answered
How can I check the default inputs by hand?
Two A, three B and one C can be arranged in 60 distinct orders.
Which rule does this calculator apply?
(a+b+c)! / (a! b! c!)