Prove that a student can attempt one or more questions out of 8 questions in `2^8 -`1 ways.

There is a question paper consisting of 15 questions. Each question has an internal choice of 3 options. In how many ways can a student attempt one or more questions of the given fifteen questions in the paper?

The number of all the possible selections which a student can make for answering one or more questions out of eight given questions in a paper, when each question has an altrenative, is

The number of all the possible selections which a student can make for answering one or more questions out of eight given questions in a paper, when each question has an altrenative, is

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

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.