Computers manufactured by a certain company have a serial number consisting of a letter of the alphabet followed by a five-digit number. If all the serial numbers of this type have been used, how many sets have already been manufactured?
26x9x9x9x9x9
2,600,000
To find the number of sets that have already been manufactured, we need to determine the total number of possible serial numbers for this type.
The company uses a single letter from the alphabet as the first digit, followed by a five-digit number.
There are 26 letters in the alphabet, so there are 26 options for the first digit.
For the remaining five digits, since they can be any digit from 0 to 9, there are 10 options for each digit.
Therefore, there are 10^5 = 100,000 possible options for the remaining five digits.
Multiplying the number of options for the first digit (26) by the number of options for the remaining five digits (100,000), we get:
26 * 100,000 = 2,600,000
Therefore, there are 2,600,000 possible serial numbers of this type.
Since all possible serial numbers have been used, it means that 2,600,000 sets have already been manufactured.
To determine the number of sets that have already been manufactured, we need to calculate the total number of possible combinations of letters and five-digit numbers.
The first part of the serial number consists of a letter of the alphabet. There are 26 letters in the English alphabet (assuming only uppercase letters are used).
The second part of the serial number consists of a five-digit number. Since it is not specified, we assume that the range of digits for each digit position is 0-9.
To calculate the total number of combinations, we multiply the number of options for each part together. In this case, we multiply 26 (options for the letter) by 10^5 (options for the five-digit number).
Therefore, the total number of combinations is: 26 * 10^5 = 26,000,000
So, if all the serial numbers of this type have been used, there would be 26,000,000 sets that have already been manufactured.