How many ordered triples (a, b, c) of positive integers are there which satisfy the equation a + b + c = 10 ?

Answer 1

if a=1, b+c=9, so 8 there
if a=2, b+c=8. so 7 there
...
if a=8, b+c=2, so 1 there
Looks like 1+2+...+8 = 36

If no duplicates are allowed, the number goes way down.

Answer 2

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