AMC 10A 2019 Problem 17

A child builds towers using identically shaped cubes of different colors. How many different towers with a height of 8 cubes can the child build with 2 rod cubes, 3 blue cubes, and 4 green cubes? (One cube will be left out.)

Answer Choices
A. 24
B. 288
C. 312
D. 1260
E. 40,320