A question paper has two parts $P\text{\hspace{0.17em}and\hspace{0.17em}}Q$ each containing 10 questions.  If a student needs to choose 8 form part $P$ and 4 from part $Q$, in how many ways can be do that?

Number of ways to choose 8 questions from part $P{=}^{10}{C}_8$

Number of ways to choose 4 questions from part $Q{=}^{10}{C}_4$

Total number of ways ${=}^{10}{C}_8{\times }^{10}{C}_4$

$=\frac{10\times 9}{2\times 1}\times \frac{10\times 9\times 8\times 7}{4\times 3\times 2\times 1}=45\times 210=9450$