Permutations & Combinations
Selection with constraints (combinations)
nta_pyq_2023_jan
Grade 11
Question:
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 Solution
Key Concept: Use cases: 0, 1, or 2 language courses selected. For each case, combine language course selection with non-language course selection.
= ⁵C₂ $\times$ ⁷C₃ + ⁵C₁ $\times$ ⁷C₄ + ⁷C₅ = 10$\times$35 + 5$\times$35 + 21 = 350 + 175 + 21 = 546.
Correct Answer: 546