# Question: Product Codes

## Comment on Product Codes

### I understand that there are

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? ### If you have 3 different

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

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? 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,

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

What you think? ### That's a perfectly valid

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 ### https://gmatclub.com/forum

https://gmatclub.com/forum/fifteen-dots-are-evenly-spaced-on-the-circumference-of-a-circle-how-194198.html 