kitchen table math, the sequel: a company labels its products...

## Wednesday, July 20, 2011

### a company labels its products...

AA2

A company labels its product with a three-character code. Each code consists of two letters (not necessarily different) from the 26 letters of the English alphabet, followed by one digit, as shown above. What is the total number of such codes that are available for labeling the company's product?

My answer is wrong, and I don't understand why.

Catherine Johnson said...

Scratch that.

I see what I did wrong.

Will post the answer in a bit.

Daniel Ethier said...

I think this is just 26x26x10 = 6760.

There is nothing tricky here that I can see. There are three slots. The first two slots are letters, with 26 possibilities each, and the last slot is a digit with 10 possibilities.

Jo in OKC said...

Anonymous said...

26×26×10

IF:

*) The order must be letter-letter-digit, and
*) The *case* of the letters doesn't count, and
*) The letters are from the Latin alphabet, and
*) The digits are base-10

All of these assumptions are quite reasonable, but if any don't hold, then the calculation above is wrong.

-Mark Roulo

Catherine Johnson said...

I absolutely can NOT take PSAT/SAT tests when I am a) hot and b) tired. CANNOT.

(Which reminds me: I have a study on sleep & performance to post.)

Somehow, I had the kind of mental block on this that I think Debbie talks about with triangle side inequalities (I've had that, too).

I figured 26 x 26 x 10, but then I was convinced I needed to divide by 26 because 26x26x10 would double count every arrangement that contained double letters.

I was mixing up the idea of "26 choose 2" and "choose 26, choose 26."

btw, it's not that I was using the wrong formula.

I actually believed that taking 26x26 overcounted "AAs" "BBs" etc.

Nata@universitiesfinancialaid said...

Thanks, I love such exersises so much! they are very useful