John has to choose 8 courses and the he has a fixed amount of courses to take, i.e. 3 out of 5 science courses, 2 out of 6 math courses and 1 out of 4 history courses. Then, the 2 courses left can be whatever out of 20-15 = 5 remaining courses.

Thus, its combinations are \(5*4*3* *6*5* *4* *5*4 = 144,000\). However, since the order in which courses are taken does not matter, we have to divide it by 3!, 2!, 1! and 2! so that we get \(\frac{144,000}{3!*2!*1!*2!} = 6000\).

Answer D