A student is  answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is:

Let first five questions form group A and remaining 8 form group B

 at least four from group $\text{ A Then,}(4A,6B)+(5A,5B)$

$\begin{array}{l}=\left({ }^5{C}_4\right.\left.{\times }^8{C}_6\right)+\left({ }^5{C}_5{\times }^8{C}_5\right)\Rightarrow \left({ }^5{C}_1{\times }^8{C}_2\right)+\left({ }^5{C}_0{\times }^8{C}_3\right)\\ =\left(5.\frac{8.7}{1.2}\right)+\left(1\cdot \frac{\mathrm{8.7.6}}{\mathrm{1.2.3}}\right)\\ =140+56=196\end{array}$