Permutations and Combinations
Combinations
JEE Main 2023
Grade 11
Question:
A boy is to select $5$ courses from $12$ available courses, of which $5$ are language courses. If he must choose at least $2$ language courses, the number of ways is:
(1) $540$
(2) $560$
(3) $596$
(4) $624$
Step-by-Step Solution
Key Concept: At least 2 language (L) from 5, at most 3 non-language (NL) from 7: $\binom{5}{2}\binom{7}{3} + \binom{5}{3}\binom{7}{2} + \binom{5}{4}\binom{7}{1} + \binom{5}{5}\binom{7}{0} = 350 + 210 + 35 + 1 = 596$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)