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?

wiskdls
Apr 21, 2018

#1**+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.

GYanggg
Apr 21, 2018

#1**+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