A pod of 6 dolphins always swims single file, with 3 females

We are given that a pod of 6 dolphins always swims single file, with 3 females at the front and 3 males in the rear. Thus:

The number of ways to arrange the 3 female dolphins in the front is 3! = 3 x 2 x 1 = 6.

The number of ways to arrange the 3 male dolphins is in the rear is 3! = 3 x 2 x 1 = 6.

Thus, the number of ways to arrange all the dolphins is 6 x 6 = 36 ways.

Answer: B

Hi ScottTargetTestPrep ,

could you quickly help me out? I do understand your explanation very well. Nevertheless, I started with the following way:


Assuming there are 6 dolphins in total, and 3 male as well as 3 female, i can assume that there are two groups (3 in each).
Applying the rules of combinatorics would leave to:

\(\frac{(6!)}{(3!)(3!)}\) . This would lead to 20 combinations.

Would you mind helping me to see what's wrong in my assumption?

Thanks!

Hi ScottTargetTestPrep ,

could you quickly help me out? I do understand your explanation very well. Nevertheless, I started with the following way:


Assuming there are 6 dolphins in total, and 3 male as well as 3 female, i can assume that there are two groups (3 in each).
Applying the rules of combinatorics would leave to:

\(\frac{(6!)}{(3!)(3!)}\) . This would lead to 20 combinations.

Would you mind helping me to see what's wrong in my assumption?

Thanks!
In this problem we don't have to choose 3 from 6 that is what you are doing.
Choosing 3 out of 6 can result in some Male and female which we don't have to do.
In this problem 3 females will be in front and 3 males will be rear.
We just have to find in how many ways females and males can arrange themselves in their own gender.

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