A test consists of 10 multiple choice questions . In how many ways can the test be answered if
(i) Each question has four choices ?
(ii) The first four questions have three choices and the remaining have five choices ?
(iii) Question number n has n + 1 choices ?

Find the total number of ways of answering five objective type questions, each question having four choices

A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected, if the team has (i) no girls (ii) atleast one boy and one girl (iii) at least three girls

An examination consists of 10 multiple choice questions, where each question has 4 options, only one of which is correct. In every question, a candidate earns 3 marks for choosing the correct opion, and -1 for choosing a wrong option. Assume that a candidate answers all questions by choosing exactly one option for each. Then find the number of distinct combinations of anwers which can earn the candidate a score from the set {15, 16,17,18, 19, 20}.

A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is