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

Answer : The question paper has two sets each containing 10 questions. So the student has to choose 8 from part A and 5 from part B.

⇒ choosing 8 questions from 10 of part A in ¹⁰C8

⇒ choosing 5 questions from 10 of part B in ¹⁰C5

⇒ by Multiplication principle, we get

= total no. of ways in which he can attempt the paper is ¹⁰C8  X10C5

= 11340 ways