In a carrom board game competition, m boys and n girls (m > n > 1) of a school participate in which every student has to play exactly one game with every other student. Out of the total games played, it was found that in 221 games one player was a boy and the other player was a girl. Consider the following statements: 1. The total number of students that participated in the competition is 30. 2. The number of games in which both players were girls is 78. Which of the statements given above is/are correct?

A schoolteacher has to select the maximum possible number of different groups of 3 students out of a total of 6 students. In how many groups any particular student will be included?

In how many different ways can four books A, B, C and D be arranged one above another in a vertical order such that the books A and B are never in continuous position?

In an examination, a question paper has 12 questions divided into Part I and Part II containing 5 and 7 questions. A student must attempt 8 questions, selecting at least 3 from each part. Number of w…

From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

Ten different letters of alphabets are given. Words with five letters are formed from these given letters. Then, the number of words which have at least one repeated letter is :