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A class has four girls and five boys. How many ways can everyone be arranged in a row, so that all four girls are next to each other?

 Apr 21, 2018

Best Answer 

 #1
avatar+972 
+2

Since all four girls are next to each other, we can treat them like one person. 

 

So it is basically a six person permutation.

 

\(6!=720\)

 

There are 720 ways to arrange the boys and girls, but we can also change the order the 4 girls sit in. 

 

\(4!=24\)

 

In total, there are \(24\cdot720=17280.\) ways to arrange everyone in a row. 

 

I hope this helped,

 

Gavin.

 Apr 21, 2018
 #1
avatar+972 
+2
Best Answer

Since all four girls are next to each other, we can treat them like one person. 

 

So it is basically a six person permutation.

 

\(6!=720\)

 

There are 720 ways to arrange the boys and girls, but we can also change the order the 4 girls sit in. 

 

\(4!=24\)

 

In total, there are \(24\cdot720=17280.\) ways to arrange everyone in a row. 

 

I hope this helped,

 

Gavin.

GYanggg Apr 21, 2018

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