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

There 10 questions in part A out of which 8 question can be chosen as = ¹⁰C₈
Similarly, 5 questions can be chosen from 10 questions of Part B as = ¹⁰C₅
Hence, total number of ways,
$$\eqalign{ & { = ^{10}}{{\text{C}}_8}{ \times ^{10}}{{\text{C}}_5} \cr & = \frac{{10!}}{{2! \times 8!}} \times \frac{{10!}}{{5! \times 5}} \cr & = \left\{ {10 \times \frac{9}{2}} \right\} \times \left\{ {\frac{{10 \times 9 \times 8 \times 7 \times 6}}{{5 \times 4 \times 3 \times 2 \times 1}}} \right\} \cr & = 11340 \cr} $$