Question: Product Codes

Comment on Product Codes

I understand that there are three different ways to arrange DDL. But I can't wrap my mind around the fact that since the digits are actually different, that when you arrange three different object there are actually 6 different ways.
So what is the logic behind the fact that there are 3 different ways with this question?
gmat-admin's picture

If you have 3 different objects to arrange, you can:
- Place the 1st object in one of 3 different locations (1st space, 2nd space and 3rd space)
- Place the 2nd object in one of the 2 remaining spaces
- Place the 3rd object in the 1 remaining space
So, the TOTAL # of arrangements = (3)(2)(1) = 6

Let's list them.
If there are three objects to arrange (A, B and C) we can create the following arrangements:
- ABC
- ACB
- BAC
- BCA
- CAB
- CBA

So why do we just count Digit1Digit2L, Digit1, L, Digit2 and L, Digit1, Digit2 as possibilities in this question, instead of the arrangements you just described?
gmat-admin's picture

I thought your question about arranging 3 objects was separate from the question on the video.
I don't quite understand your latest question. Can you please rephrase it?

Hi Brent,

In your second solution, we can solve using following way,

1. Select 2 Digit can also be solved as if order of two digit is important then it can be done = 5*4=20
2.Select One letter = 6
3. Arrange selected Letter in specific 2 digit by keeping order of digit important, this can be done in 3 ways, for ex if digit is 71 and letter is E then E can be placed as E71, 7E1, 71E. So a arrange letter in specific digit can be done =3

So answer is = 20*6*3=360.

What you think?

gmat-admin's picture

That's a perfectly valid approach - nice work!

That's what I love about GMAT math questions. They can often be solved in many different ways.

https://gmatclub.com/forum/given-that-there-are-5-basketball-players-per-team-how-many-ways-can-219484.html
sir please explain

https://gmatclub.com/forum/fifteen-dots-are-evenly-spaced-on-the-circumference-of-a-circle-how-194198.html
please explain
gmat-admin's picture

Add a comment

Office Hours

Have questions about your preparation or an upcoming test? Need help modifying the Study Plan to meet your unique needs? No problem. Just book a Skype meeting with Brent to discuss these and any other questions you may have. 

Change Playback Speed

You have the option of watching the videos at various speeds (25% faster, 50% faster, etc). To change the playback speed, click the settings icon on the right side of the video status bar.

Have a question about this video?

Post your question in the Comment section below, and I’ll answer it as fast as humanly possible.

Free “Question of the Day” emails!