JEE Main · 2023 · 24 Jan 2023 · Shift 2 · Permutations and Combinations

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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

Answer: 546

Solution

With

5

language courses and

7

non-language courses, choosing at most two language courses splits into three cases. No language course gives

(0 5) (5 7) = 21

, one language course gives

(1 5) (4 7) = 175

, and two language courses give

(2 5) (3 7) = 350

. The total is

21 + 175 + 350 = 546.

JEE Main · 2023 · 24 Jan 2023 · Shift 2 · Integer answer

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