AMC 10A 2016 Problem 20

For some particular value of N, when (a+b+c+d+1)^{N} is expanded and like terms are combined, the resulting expression contains exactly. 1001 terms that include all four variables, a, b, c, and d, each to some positive power. What is N ?

Answer Choices
A. 9
B. 14
C. 16
D. 17
E. 19