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  • How many different ways are there to arrange a row of five girls and six boys so that the four girls sit together?Option: 1 12096

How many different ways are there to arrange a row of five girls and six boys so that the four girls sit together?

Option: 1

120960

 


Option: 2

220380


Option: 3

967680

 


Option: 4

850480


Answers (1)

Given that,

There are 5 girls and 6 boys.

Let us treat the block of four girls as a single entity. 

Then we have 8 entities to arrange: {block of 4 girls}, {girl}, {boy}, {boy}, {boy}, {boy}, {boy},{boy}. 

There are 8! ways to arrange these entities.

Within the block of 4 girls, there are 4! ways to arrange the girls. 

Therefore, the total number of arrangements in which the four girls sit together is:

8!\times 4!=967680

So there are 967680 different ways to arrange the row of five girls and six boys so that the four girls sit together.

 

Posted by

Ramraj Saini

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