Im very confused on his, please show work and explain.

Problem 2 (5 pts): How many solutions are there to the equation x1 + x2 + . . . + x7 = 40, (a, for 1 pt.): where the ai's are nonnegative integers? (b, for 2 pts 3? (c, for 2 pts.): where the a,'s are nonnegative integers and x4,x5, T6,7 are positive? S.): where the x's are nonnegative integers and T1