I am a little confused by this question.Find the number of integral solutions of x1 + x2 + x3 + x4 = 28

where each xi ≥ 1, and in addition each xi ≤ 8. Write your answer in terms of binomial coefficients.

My solution would be to take the number of solutions where xi ≥ 1. Then I would subtract from that the total number of solutions where xi ≥9. This would leave the number of solutions where xi ≥ 1, and in addition each xi ≤ 8.

But when I try to find solutions where xi ≥9 I realized this is not possible.

Could someone give me a nudge in the right direction (without giving the answer).

Thanks