A boy needs to select five courses from 12 available… — JEE Main 2023 Mathematics PYQ

JEE Main 2023 · 24 Jan · Shift 1 · Paper-1(B.E./B. Tech.) · numerical answer

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 __________

Show answer and solution

Answer: 546

Solution

We need to count selections of 5 courses from 12 (5 language + 7 non-language) with at most 2 language courses.

Cases:
- 0 language: C(5,0)×C(7,5) = 1×21 = 21
- 1 language: C(5,1)×C(7,4) = 5×35 = 175
- 2 language: C(5,2)×C(7,3) = 10×35 = 350

Total = 21 + 175 + 350 = 546

[JEE Main 2023 · 24 Jan · Shift 1 · Paper-1(B.E./B. Tech.)]

Practise Permutations and Combinations the way it is asked

A timed set of real JEE Main Permutations and Combinations questions, graded as the exam grades. No sign-up.

Start a Permutations and Combinations test

More: all JEE Main Permutations and Combinations questions · JEE Main 2023 · Mathematics chapter list

JEE Main 2023 Mathematics question on Permutations and Combinations