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## Homework Statement

# of integer solutions of x1+x2+x3+x4 = 32

where x1,x2,x3>0 and 0<x4≤25

## Homework Equations

## The Attempt at a Solution

So in the case where x4 = 25 we have

x1+x2+x3= 4

in the case where x4 = 24 we have

x1+x2+x3 = 5

.....

in the case where x4 = 1 we have

x1+x2+x3 = 28

so we can do x1+x2+x3+x4 = 28

which will give us f = 31!/3!28!

now we subtract f - g where g =

x1+x2+x3 < 4

(31!/(3!28!)) - (6!/(3!3!))

= 4475

The answer is correct but I don't know if my method is a good one. Can anyone let me know?