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

A boy needs to select 5 courses from 12, of which 5 are language courses. He can choose at most 2 language courses.

The remaining 12 - 5 = 7 courses are non-language courses.

Case 1: 0 language courses.

$$\binom{7}{5} = 21$$

Case 2: 1 language course.

$$\binom{5}{1} \times \binom{7}{4} = 5 \times 35 = 175$$

Case 3: 2 language courses.

$$\binom{5}{2} \times \binom{7}{3} = 10 \times 35 = 350$$

Total = 21 + 175 + 350 = 546

The answer is 546.