Combinations or Fundamental Counting

melguy wrote:Hi Brent

I was going through your videos. I have some confusion in this video and would appreciate your help https://www.gmatprepnow.com/module/gmat ... /video/795

At 1:20 you mention that the "outcomes are different". I am a bit confused with the language. We can find the result by using the solution attached. But in what scenarios would the choice of man affect the choice of selecting woman (or may be affect the order). The end result will be 2 men and 2 women.

Thanks

Hi melguy,

That question is basically a follow-up to this lesson (https://www.gmatprepnow.com/module/gmat ... /video/788) where we discuss how to determine when we can the Fundamental Counting Principle (FCP) and when we must use other counting techniques (typically combinations).

So, let's say we start by taking the task of selecting 2 men and 2 women for the committee and break it into stages (in the hopes that we can use the FCP).
Let's say our first stage is: select a man and our second stage is: select another man.
At this point, we should ask "Is the outcome of stage 1 different from the outcome of stage 2?"
The answer here is no. The man selected in stage 1 gets to be on the committee, and the man selected in stage 2 gets to be on the committee. The two outcomes are identical. As such, we cannot use the FCP in this matter otherwise we'll end up over counting some outcomes. For example, selecting Joe in stage 1 and selecting Bob in stage 2 is exactly the same as Bob in stage 1 and selecting Joe in stage 2.

The solution that you suggest (involving combinations) is the same as the solution that we have in the video.
Notice that we changed the strategy so that we were still able to use stages (and the FCP), but we had to change the way we broke the task into stages.

I hope that helps.

Cheers,
Brent

melguy wrote:Thanks for the clarification.

BTW excellent collection of videos! I used your videos in my prep last time also. There are some great tips and tricks i picked during the learning process from your videos.

Glad you liked them!