[NOIP2017 Popularization Group] Three students, A, B, and C, take elective courses. From the 4 courses, A takes 2 courses, and B and C each take 3 courses. There are ( ) different elective plans.

topic

[NOIP2017 Popularization Group] Three students, A, B, and C, take elective courses. From the 4 courses, A takes 2 courses, and B and C each take 3 courses. There are ( ) different elective plans.
A.36 B.48 C.96 D.192

answer

$$C_4^2\times C_4^3\times C_4^3=\frac{4\times 3}{2}\times \frac{4\times 3\times 2}{3\times 2}\times \frac{4\times 3\times 2}{3\times 2}$$
$$\frac{4\times 3}{2}\times \frac{4\times 3\times 2}{3\times 2}\times \frac{4\times 3\times 2}{3\times 2}=\frac{4\times 3\times 4\times 3\times 2\times 4\times 3\times 2}{2\times 3\times 2\times 3\times 2}$$
$$\frac{4\times 3\times 4\times 3\times 2\times 4\times 3\times 2}{2\times 3\times 2\times 3\times 2}=\frac{4\times 3\times 4\times 4}{2}$$
$$\frac{4\times 3\times 4\times 4}{2}=2\times 3\times 4\times 4=96$$
Why Choose C.96