In an
examination, a question paper consists of 12 questions divided into
two parts i.e., Part **I** and Part **II**, containing 5 and 7
questions, respectively. A student is required to attempt 8 questions
in all, selecting at least 3 from each part. In how many ways can a
student select the questions?

It is
given that the question paper consists of 12 questions divided into
two parts – Part **I** and Part **II**, containing 5 and
7 questions, respectively.

A student has to attempt 8 questions, selecting at least 3 from each part.

This can be done as follows.

(a) 3
questions from part** I** and 5 questions from part **II**

(b) 4
questions from part **I** and 4 questions from part **II**

(c) 5
questions from part** I** and 3 questions from part **II**

3
questions from part** I** and 5 questions from part **II **can
be selected in
ways.

4
questions from part **I** and 4 questions from part **II** can
be selected in
ways.

5
questions from part **I** and 3 questions from part **II** can
be selected in
ways.

Thus, required number of ways of selecting questions

**
**