Verified Solution • 2025–26 Session moderate

QJEEM23Ma08f1: JEE Main 2023 Mathematics - Class 11 JEEM23Ma08f1 Solution: A boy needs to select five courses from 12 available courses,…

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 __________

Step-by-Step Verified Solution

Among 12 courses, 5 courses are of language.

∴ Remaining 7 are different courses.

Now, number of ways to select 5 courses where at most 2 language courses present.

Language Different Number of ways
Case 1 0 5 5C0×7C5
Case 2 1 4 5C1×7C4
Case 3 2 3 5C2×7C3

∴ Total number of ways

=5C0×7C5+5C1×7C4+5C2×7C3

=546

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