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for example 9 into 3 parts

x+y+z=9

and each element must be non zero , first look tells me it's combination with repetition.

however C(n-1,n-k) doesn't give the same number of possibilities when trying all of them.

x+y+z=9 C(8,6)=28

while trying them give only 7 possibilities

(7,1,1) (6,2,1) (5,2,2) (5,3,1) (4,4,1) (4,3,2) (3,3,3)

(1,7,1) is the same as (1,1,7) and (7,1,1) this small condition is changing the outcome , what kind of problem is this called ?