We have three males and three females to order. Let's consider them in order.
First male we line up: we have 3 possibilities.
First female we line up: we have 3 possibilities.
Second male we line up: we have 2 possibilities (one male was already assigned to the first male position).
Second female we line up: we have 2 possibilities
Third male we line up: 1 possibility (the only male left).
Third female we line up: 1 possibility (only female left).

By property, we need to multiply these choices : overall we have 3 * 3 * 2 * 2 * 1 * 1 = 36.

There may be a more efficient way though...

Take the task of lining up the 6 competitors and break it into stages.

Stage 1: Select a competitor for the 1st position
This person must be a male.
Since there are 3 males to choose from, we can complete stage 1 in 3 ways

Stage 2: Select a competitor for the 2nd position
This person must be a female.
Since there are 3 females to choose from, we can complete stage 2 in 3 ways

Stage 3: Select a competitor for the 3rd position
This person must be a male.
There are 2 males remaining to choose from (since we already selected a male in stage 1), so we can complete stage 3 in 2 ways

Stage 4: Select a competitor for the 4th position
This person must be a female.
There are 2 females remaining to choose from. So we can complete stage 4 in 2 ways

Stage 5: Select a male for the 5th position
There's only 1 male remaining. So we can complete stage 5 in 1 way

Stage 6: Select a female for the 6th position
There's only 1 female remaining. So we can complete stage 6 in 1 way

By the Fundamental Counting Principle (FCP), we can complete all 6 stages (and thus create a 6-person lineup) in (3)(3)(2)(2)(1)(1) ways (= 36 ways)

Answer: D

Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.

RELATED VIDEOS

Adding to this answer is the question:
When can we use the Fundamental Principle of Counting?


When? When the number of outcomes for each stage is independent of the other stages. In this case it is. That is for example, no matter what male we choose in stage 1, there will always be 3 outcomes to choose from in stage 2, 2 outcomes to choose from in stage 3, and so on.

For example in what case would you not be able to use Fundamental Principle of Counting?

Let's say
Males: Mike, Marco, and Mills
Females: Jess, Jill, Gina

Suppose we had the requirement that if we choose Mike in Stage 1 we can only choose Jess and Jill in stage 2, and if we choose Marco or Mills in stage 1 we can choose any of the girls in stage 2.

Then here we wouldn't be able to use Fundamental Principle of Counting, because the number of outcomes of the stages are not independent of each other. If Mike is chosen we only have 2 possible outcomes in Stage 2, and if we choose Marco or Mills we have 3 possible outcomes in Stage 2.

The order has been specified in the question stem, arrange accordingly.
we need an Alternate MFMFMF.
each male and female and arrange themselves 3! ways, hence total arrangements =3!*3!.

Why isn't it 6!
[/quote]

If you explain your rationale for concluding the answer is 6!, I'm sure someone on this forum can help.

Bump for further discussions