Question on Num Properties - Combinatorics

[TiffanyReynolds3]

On Page. 53 (Combinatorics) (5th ed. - Num Properties) Chapter 3 Problem 4:

A pod of dolphins always swim in single file, with 3 females at the front and 3 females in the rear. In how many different arrangements can the dolphins swim?

I understand the multiple groups piece and how we multiple female arrangements * male arrangements, but am struggling conceptually with why we are not taking into consideration order? I don't understand why there are only 3! ways in which the females can swim? There are 3 ways in which females can be first in the line but then, the 2nd and 3rd dolphin can switch spots. Let's say there are dolphins S, A, and M.

S M A
A S M
M A S

but they could also be

S M A
M A S
A S M

What am I missing here?

[StaceyKoprince]

Please remember to read the forum guidelines before posting. This folder is only for general strategy questions, not content or specific test problems.

Check out the content / problem folders and post in the relevant folder depending upon the source of the problem you want to post (and make sure to follow the rules about banned sources). This problem would go in the MGMAT non-CAT quant folder.

Please also make sure you proof your post; the problem is missing a key detail (it's impossible to solve without that detail) and we don't always have access to the books while we're answering posts. Thanks!

Here's the actual problem:
A pod of 6 dolphins always swims single file, with 3 females at the front and 3 males in the rear. In how many different arrangements can the dolphins swim?

You're totally right that there are 6 possible ways for the 3 female dolphins to be arranged. The term 3! means 3 * 2 * 1, which equals 6. I'm guessing you were just mis-reading 3! as plain old 3?

Let me know if that clears up the issue!