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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
Correct Answer: 546
12 courses (5 language, 7 non-language), choose 5 with at most 2 language.
0 language: $$\binom{7}{5} = 21$$. 1 language: $$\binom{5}{1}\binom{7}{4} = 175$$. 2 language: $$\binom{5}{2}\binom{7}{3} = 350$$.
Total = 21 + 175 + 350 = 546.
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