1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
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?

A
The number of arrangements in which two chemistry books are separated is 9×10!
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
The number of arrangements in which four physics books are together is 8! 4!
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
The number of arrangements in which no two mathematics books are together is (76)(6!)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
The number of arrangements in which the books of the same subject are all together is 12(4!5!)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
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
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program