PnC 6-DISTRIBUTION & PARTITION RULE || Quantitative Aptitude || CAT 2021 || 23 October

In how many ways seven different books be distributed to two persons if each person receives at least one book?

There are six teachers. Out of them, two teach physics, other two teach Chemistry and the rest two teach Mathematics. They have to stand in a row such that Physics, Chemistry and Mathematics teachers are always in a set. The number of ways in which they can do, is :

Seven books including 2 identical Social Science books, 2 different Chemistry books, 2 different English books and 1 bio books are to be arranged on a book shelf. If Social Science books are to be kept together, position of Chemistry books can’t be extreme left or extreme right and English books are to not to be together, how many ways can the arrangement be made?

Find the total number of ways in which a student can attempt an exam, such that he answers at least two questions out of a total of 150 questions in the exam, given that each question has four multiple answers choices.

In a school team of 10 athletic player and 5 strength based players, 5 students are to be selected to the state team so that at least 3 athletic player and 1 strength based player are there in the state team. In how many ways can it be done?