A question paper has two parts, A and B, each containing 10 questions. If a student has to choose 5 from part A and 8 from part B, in how many ways can he choose the questions?

Question: A question paper has two parts, A and B, each containing 10 questions. If a student has to choose 5 from part A and 8 from part B, in how many ways can he choose the questions?

Solution:
ways to choose 5 from part A = ¹⁰C₅
ways to choose 8 from part B = ¹⁰C₈

choose 5 from part A and 8 from part B = ¹⁰C₅ × ¹⁰C₈
= {10!/(5! 5!)} × {10!/(2! 8!)}
= 11340