  Question

# A total of 5 different mathematics books, 4 different physics books and 2 different chemistry books are to be arranged in a row in a book shelf. Which of the following is (are) TRUE?The number of arrangements in which two chemistry books are separated is 9×10!The number of arrangements in which four physics books are together is 8! 4!The number of arrangements in which no two mathematics books are together is (7⋅6)(6!)The number of arrangements in which the books of the same subject are all together is 12(4!⋅5!)

Solution

## The correct options are A The number of arrangements in which two chemistry books are separated is 9×10! B The number of arrangements in which four physics books are together is 8! 4! D The number of arrangements in which the books of the same subject are all together is 12(4!⋅5!)Total number of arrangements =11! Number of arrangements that two chemistry books are together =2!×10! Hence, number of arrangements that two chemistry books are separated =11!−2!×10!=9×10! Number of arrangements in which four physics books are together =8! 4! since four physics books can also be permuted among themselves in 4! Similarly, number of arrangements in which the books of the same subject are all together =3!(5! 4! 2!)=12(4!⋅5!) We want no two mathematics books should be together. So, let us first place the other six books. __  __  __  __  __  __ This can be done in 6! ways as there are six blanks. Now, we can put mathematics books between these 7 gaps. This can be done in 7C5×5! Hence, number of arrangements in which no two mathematics books are together is 6!×7C5×5!  Suggest corrections   