The number of ways 5 English books and 4 Hindi books can be placed on a shelf so that the books on the same language always remain together is (a) \(5 ! 4 ! 3 !\) (b) \(5 ! 4 ! 2 !\) (c) \(4 ! 3 ! 2 !\) (d) \(5 ! 3 ! 2 !\)

Short Answer

Expert verified
(b) \(5! 4! 2!\)

Step by step solution

01

Arrange English books

Firstly, arrange the 5 English books among themselves. The number of ways to arrange n items is given by \(n!\). So the 5 English books can be arranged in \(5!\) ways.
02

Arrange Hindi books

Then, arrange the 4 Hindi books among themselves. Similarly, the 4 Hindi books can be arranged in \(4!\) ways.
03

Arrange the batches

Now, consider the batch of English books and the batch of Hindi books as two separate objects. These two objects can be arranged among themselves in \(2!\) ways.
04

Get the total arrangements

Finally, to get the total number of arrangements, multiply the number of arrangements of the English books, the Hindi books and the two batches among themselves: \(5! * 4! * 2!\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Study anywhere. Anytime. Across all devices.

Sign-up for free