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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 ____________

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answer is 546.

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Detailed Solution

Languages (5)	Other (7)	combinations
2	$3$	$5_{C_{2}} \cdot 7_{C_{3}} = 350$
1	$4$	$5_{C_{i}} \cdot 7_{C_{4}} = 175$
0	$5$	$5_{C_{0}} \cdot 7_{C_{5}} = 21$
total = 546

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