Posted by **Mike** on Monday, February 14, 2011 at 10:15pm.

Computers manufactured by a certain company have a serial number consisting of a letter of the alphabet followed by a six-digit number. If all the serial numbers of this type have been used, how many sets have already been manufactured?

- math -
**MathMate**, Monday, February 14, 2011 at 10:26pm
Since there are *always* 2 letters and 6 digits, and the order of the letters and digits *do* matter, it is a question of permutations.

We take the letters and digits in sequence, and multiply together the possible choices for each:

First letter: 26

Second letter: 26

digit 1: 10

digit 2: 10

digit 3: 10

digit 4: 10

digit 5: 10

digit 6: 10

So the number of computers manufactured if all numbers have been used is:

26²*10^{6}.

- math -
**Mike**, Monday, February 14, 2011 at 10:37pm
so the answer is 676,000,000 sets?

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**MathMate**, Monday, February 14, 2011 at 10:39pm
Correct.

However, teachers would like to see how your number was obtained. Do NOT *just* give a numerical result. Most of the time, the numerical number is less interesting (to the teacher).

- math -
**Ralph**, Monday, March 28, 2011 at 5:36pm
Above is wrong. It says 1 Letter and 6 digits. so answer is 26 * 10^6 or 26,000,000

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