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  4. 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 eourses is

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Q. 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 eourses is

JEE MainJEE Main 2023Permutations and Combinations

Solution:

For at most two language courses
$={ }^5 C _2 \times{ }^7 C _3+{ }^5 C _1 \times{ }^7 C _4+{ }^7 C _5=546$