New Girl in the City.

She has 4 pink and 4 blue bags.

• She can permute the 4 blue bags in 4! ways.

• She can permute the 4 pink bags in 4! ways.

• Each even bag can either be blue or pink.

So, there are a total of 2(4!4!) ways

Let the arrangement starts with pink bag, since we have $n$ pink bags placed alternately so number of ways to arrange them $= n!$

and number of ways to arrange $n$ blue bags $= n!$

and the other way to arrange the bags is by starting with a blue bag.

hence total number of ways of arranging the bags in a row so that neighboring bags are of different colors is $= 2\times n!\times n!$ $=1152$

therefore $n=4$

hence total number of bags the girl is having $=8$

Since there are the same number of $\color{#E81990}{pink}$ and $\color{#3D99F6}{blue}$ bags, there are $\dfrac{1152}{2}=576$ arrangements starting with a $\color{#3D99F6}{blue}$ bag. Since the $\color{#3D99F6}{blue}$ and $\color{#E81990}{pink}$ bags can be arranged independently in the same number of ways (let's call it $w$ ) we can say

$w=\sqrt{576}=24$

So the number of $\color{#3D99F6}{blue}$ bags can be arranged in $24$ ways.

It is now easy to run through the first few factorials to see that

$4!=24$

So there are 4 $\color{#3D99F6}{blue}$ bags and $\boxed{8}$ $\color{#3D99F6}{b}$ $\color{#E81990}{a}$ $\color{#3D99F6}{g}$ $\color{#E81990}{s}$ in total.