A boy needs to select five courses from 12 available courses, out of which 5 courses are l…

Question

A boy needs to select five courses from 12 available courses, out of which 5 courses are language courses. If he can choose at most two language courses, then the number of ways he can choose five courses is:

Answer: 546

Accepted Answer

At most 2 language courses out of 5, and the rest from 7 non-language courses:

$$\binom{5}{2}\binom{7}{3} + \binom{5}{1}\binom{7}{4} + \binom{5}{0}\binom{7}{5} = 10\times35 + 5\times35 + 1\times21 = 350+175+21 = 546$$

Solutions · 1