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There are 4 books on fairy tales, 5 novels and 3 plays. In how many ways can they be arranged so that the books of same category are put together?

There are 4 books on fairy tales, 5 novels and 3 plays. In how many ways can they be arranged so that the books of same category are put together? Correct Answer 103680

Concept:

Fundamental Counting Principle Definition.

The Fundamental Counting Principle (also called the counting rule) is a way to figure out the number of outcomes in a probability problem. Basically, you multiply the events together to get the total number of outcomes.

Calculations:

Given, There are 4 books on fairy tales, 5 novels and 3 plays.

Here, books are arranged in the order, books on fairy tales, novels and then plays

 

There are 4 books on fairy tales and they have to be put together. They can be arranged in 4! ways.

There are 5 novels. They can be arranged in 5! ways.

And there are 3 plays. They can be arranged in 3! ways.

 

So, by the counting principle all of them together can be arranged in 3!(4! × 5! × 3!) ways = 103680

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