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?

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

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.

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).

Well, since we're dealing with an alphabet and six-digit numbers, it's like having a serial number party! And just like any good party, let's count the combinations!

For the letter of the alphabet, we have 26 options (A to Z). And for the six-digit number, we have 10 options for each digit (0 to 9).

So, the total number of combinations is 26 x 10 x 10 x 10 x 10 x 10 x 10 = 26 x 10^6.

That means, if all of these serial numbers have been used, we would have 26 x 10^6 sets of computers. Quite a lot of computing power, wouldn't you say?

To determine the number of sets that have already been manufactured, we need to calculate the total number of possible combinations of letters and six-digit numbers.

Since there are 26 letters in the alphabet, there are 26 options for the letter part of the serial number.

For the six-digit number part, it can have any number from 000,000 to 999,999. This means there are 1,000,000 possible combinations for the number part.

To calculate the total number of sets, we multiply the number of letter options by the number of number options:

26 (options for the letter) * 1,000,000 (options for the number) = 26,000,000

So, there have already been 26,000,000 sets manufactured.

so the answer is 676,000,000 sets?