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Home » In an examination, a student has 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 the choice.
In an examination, a student has 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 the choice.
CBSE | Class 11 | Maths | NCERT Exemplar | Permutations and Combinations
In an examination, a student has 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 the choice.

Solution:

It is known that,

=\frac{{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}}{\mathrm{r} !(\mathrm{n}-\mathrm{r}) !}

As per the question,

5 = Total no. of questions

4 = No. of questions to be answered

Question number 1 and 2 are compulsory questions.

As a result, the no. of ways in which the student can make the choice ={ }^{3} \mathrm{C}_{2} { }^{3} \mathrm{C}_{2}=3 ! /(2 ! 1 !)=3 ways.

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