JEE Main 2023 (Online) 24th January Morning ShiftQuestion 1
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
Permutation and Combination
Answer$546$
Solution
Formulas used. (1) $\binom nr$ selectionsStep 1 - Courses. 5 language, 7 other. Step 2 - Cases. 0 language: $\binom75=21$. 1 language: $\binom51\binom74=175$. 2 language: $\binom52\binom73=350$. Step 3 - Total. $21+175+350=546$. Answer: 546