Given:
Total number of questions
![\[=\text{ }5\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e45ddd13b94c34a71f1a55ef7d8c9ef2_l3.png "Rendered by QuickLaTeX.com")
Total number of questions to be answered
![\[=\text{ }4\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c3eb383e81fbe00df56991781bcd9be4_l3.png "Rendered by QuickLaTeX.com")
Number of ways = we need to answer 2 questions out of the remaining 3 questions as 1 and 2 are compulsory.
![\[={{~}^{3}}{{C}_{2}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-415ec84dc32d2c054745c0f4f3a2735c_l3.png "Rendered by QuickLaTeX.com")
By using the formula,
![\[^{n}{{C}_{r}}~=\text{ }n!/r!\left( n\text{ }-\text{ }r \right)!\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8cb2d5b7f61733447dfe2e68eac67f32_l3.png "Rendered by QuickLaTeX.com")
![\[^{3}{{C}_{2}}~=\text{ }3!/2!\left( 3\text{ }-2 \right)!\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-51bf907fc98d0d289d0e3e38ee72dbdd_l3.png "Rendered by QuickLaTeX.com")
Or,
![\[=\text{ }3!\text{ }/\text{ }\left( 2!\text{ }1! \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b8ba41ee2ea51d0d1eb06e4bf19e0959_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }\left[ 3\times 2\times 1 \right]\text{ }/\text{ }\left( 2\times 1 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2531f333c1f8cb9767245e0839398074_l3.png "Rendered by QuickLaTeX.com")
So,
![\[=\text{ }3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e8fbed5bab4c1b1ac15d440056d7f326_l3.png "Rendered by QuickLaTeX.com")
∴ The no. of ways answering the questions is
![\[3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-df8bcc09db12acd0f6bda88b4b8135fb_l3.png "Rendered by QuickLaTeX.com")
