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# math

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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?

wiskdls  Apr 21, 2018

#1
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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
Sort:

#1
+619
+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