7. In many applications, it turns out that we are interested in finding integers x1, x2, , xr such that x1 + x2 + + xr = n, where r and n are fixed positive integers.

(a) If x1, x2, , xr are restricted to being strictly positive, how many distinct solutions does the above equation have? (Hint: Think of lining up n objects and placing an appropriately chosen number of dividers between the objects.)

(b) If x1, x2, , xr are restricted to being nonnegative, how many distinct solutions does the above equation have? (Hint: Use part 7a intelligently.)