Suppose that an exam has 34 questions on it and students nee

Suppose that an exam has 34 questions on it and students need to answer 27 of the questions. In how many ways can this be done if exactly 6 of the first 9 questions and the last 11 questions must be answered and question #14 must not be answered because of a typo?

Solution

Total questions = 34

To be answered = 27

6 out of 9 questions can be answered in 9C6 ways

11 questions answered in 1 way

Remaining questions are 14 and answers are 7

As 14 cannot be answered

available questions = 13 to be answered =7

This can be done in 13C7 ways

Total no of ways answered = 9C6 (13C7) ways