Question

In an examination a student has to answer 5 questions, out of 9 questions in which 2 are compulsory. In how many ways a student can answer the questions?

Answer 1

Total number of questions = 9

Number of questions to be answered = 5

Since 2 questions are compulsory

A student must select 3 questions from dying remaining 7 questions

The number of ways of selecting 3 questions from 7 questions is = 7C₃

∴ The number of ways of answering 5 questions = 7C₃

= `(7!)/(3!(7 - 3)!)`

= `(7!)/(3! xx 4!)`

= `(7 xx 6 xx 5 xx 4!)/(3! xx 4!)`

= `(7 xx 6 xx 5)/(3!)`

= `(7 xx 6 xx 5)/(3 xx 2 xx 1)`

= 7 × 5

= 35