# math

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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 -

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*106.

• math -

so the answer is 676,000,000 sets?

• math -

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 -

Above is wrong. It says 1 Letter and 6 digits. so answer is 26 * 10^6 or 26,000,000