Find the total number of all possible selections of one or more questions from 12 given questions, each question having an alternative also.

A question paper consists of two sections having respectively, 3 and 5 questions. The followinng note is given on the paper "it is not necessory to attempt all the questions one questions from each section is compulsory". In how many ways can candidate select the questions?

Find the total number of 9-digit numbers which have all different digits.

An instructor has a question bank consisting of 300 easy True / False questions, 200 difficult True / False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question?

A question paper consists of two sections having respectively 3 and 4 questions. The following note is given on the question paper : "It is not necessary to attempt all the questions. One question from each part is compulsory.”’ In how many ways Can a candidate select the questions ?

In a multiple choice questions there are four alternative answers, of which one or more correct. A candidate will get marks in the question only if the ticks all the correct answers. The candidate decides to tick answers at random. If the is allowed upto three chances to answer the question, find the probability that he will get marks in the questions.

In an examinations there are three multiple choice questions and each questions has 4 choices. Find the number of ways in which a student can fail to get all answer correct.