Login/Sign Up
Home » In an examination, a student to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make a choice.
In an examination, a student to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make a choice.
CBSE | Class 11 | Combinations | Exercise 17.2 | Maths | RD Sharma
In an examination, a student to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make a choice.

Given:

Total number of questions

    \[=\text{ }5\]

Total number of questions to be answered

    \[=\text{ }4\]

Number of ways = we need to answer 2 questions out of the remaining 3 questions as 1 and 2 are compulsory.

    \[={{~}^{3}}{{C}_{2}}\]

By using the formula,

    \[^{n}{{C}_{r}}~=\text{ }n!/r!\left( n\text{ }-\text{ }r \right)!\]

    \[^{3}{{C}_{2}}~=\text{ }3!/2!\left( 3\text{ }-2 \right)!\]

Or,

    \[=\text{ }3!\text{ }/\text{ }\left( 2!\text{ }1! \right)\]

    \[=\text{ }\left[ 3\times 2\times 1 \right]\text{ }/\text{ }\left( 2\times 1 \right)\]

So,

    \[=\text{ }3\]

∴ The no. of ways answering the questions is

    \[3\]

i

More Material