Question: 2 Men and 2 Women

Comment on 2 Men and 2 Women

Brent, I don't understand what you mean by "outcome" when analyzing whether or not to use the combination formula. Grateful for your assistance on this.
gmat-admin's picture

That's a common/tricky question. If it's okay, I'd like to refer you to this video:

Also, I wrote an article about this as well:

After reviewing these resources, please let me know if you need additional help.

Dear Brent, I used different approach and surprisingly the outcome is same.

1. I break down into 4 stages of committee
2. Use FCP : 4 X 3 (for women) X 6 X 5 (for men) and then divided by 2 X 2 (because order of each woman-woman and man-man combination are not matter).
3. The result is 90.

Is it okay to use this approach?
gmat-admin's picture

That's a perfectly valid approach - nice work!

Hi Brent- In last problem "Bicycle with Optional Features ", we added result of combination but in this problem we used counting principle, so how to decide when to add combination result and when to multiply it?
gmat-admin's picture

We solved the "Bicycle with Optional Features" ( in two different ways. The first (and best) way used the Fundamental Counting Principle and multiplied the stages. In the second solution, we basically just proved a general principle.

How did you get the answers so quickly at the end ? 6C2 and 4C2? Was there a shortcut that i missed in an earlier video?
gmat-admin's picture

Here's the video on calculating combinations (like 6C2 and 4C2) in your head:


Hi Brent,
In your video, you mentioned that the outcome didn’t matter in choosing 2 men and choosing 2 women but it did so between selecting the men and women. So you applied FCP to get 90.

But how can we assume that the outcome matters when choosing the stages between men and women? The question says the committee must consist of exactly 2 men and 2 women.
So, The below arrangement satisfies also satisfies the question :
#1, man woman man woman
#2 Woman Man Man Woman
And so on..
gmat-admin's picture

The first thing we need to recognize is that the outcome of selecting two men is different from selecting the outcome of selecting two women.

This means we can use the FCP and set up our stages as:
STAGE 1: Select two men
STAGE 2: Select two women

At this point, when we tackle STAGE 1, we need to recognize that the outcome of selecting Man X first, is the SAME as the outcome of selecting Man X second.
So, when calculating the number of outcomes for STAGE 1, we can't use the FCP.
Instead we must use combinations.

Does that help?

Hi Brent,

I am not still not clear.

Could you please explain how the outcome is different for men and women. The question asks for a 4 person committee with 2 men and 2 women. Men and Women are persons right? How is the gender alone creating a different outcome?

For instance, if the question asked us to form a 4 person committee with 2 tall men and 2 short women, then I would understand the outcomes would matter.

Thank you for your help with this.
gmat-admin's picture

Although the men and women are both humans, the context of the question tells us that they are considered different.
If the question said the committee needed to have 4 humans, then the answer would be 10C4.

Here's another way to think of it:
Let's say we have 2 women and 2 men. In how many ways can we create a committee of 2 women?
Since the question specifically asks for 2 WOMEN, there's only 1 possible outcome.

Does that help?

How many different handshakes are possible if six girls are standing on a circle and each girl shakes hands with every other girl except the two girls standing next to her?

Can I do 6c2-4c2 = 9( Total - breaking restns)
gmat-admin's picture

Your calculations yield the correct answer, but I'm not entirely sure what 4C2 represents.
Can you elaborate?

In the meantime, here's how I would answer this question:
There are 6 girls, and EACH girl shakes hands with 3 girls.
6 x 3 = 18.

However, we need to realize that our calculation of 18 includes duplicates.
For example, when girls B and E shake hands, girl B counts this as 1 of her 3 handshakes, AND girl E counts this as 1 of her 3 handshakes.
In other words, that 1 handshake has been counted 2 times.
In fact, every handshake has been counted 2 times.
To account for this duplication will divide 18 by 2 to get 9.

Can you explain how to use statement 2 here? thanks!

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