In an examination, a student has to answer 4 questions out of 5
Question:

In an examination, a student has to answer 4 questions out of 5. Questions 1 and 2 are compulsory. Find the number of ways in which the student can make a choice.

Solution:

A student has to answer 4 questions out of 5 in which he is compelled to do the 1 and 2 questions compulsory. So he has to attempt 2 questions from 3 of his choice.

Choosing 2 questions from 3 will be in ${ }^{3} \mathrm{C}_{2}$ ways.

Applying ${ }^{n} C_{r}=\frac{n !}{r !(n-r) !}$

$=3$ ways.