Serial numbers for a product are to be made using
3
letters followed by
4
numbers. If the letters are to be taken from the first
8
letters of the alphabet with repeats possible and the numbers are taken from the digits
0
through
9
with no repeats, how many serial numbers can be generated?
This is not a geography question.
To find the number of serial numbers that can be generated, we need to determine the number of choices for each position in the serial number.
For the letters, we are selecting 3 letters from the first 8 letters of the alphabet with repeats possible. This can be calculated using the concept of combinations with repetition. The number of choices for each letter is 8 since we are selecting from the first 8 letters of the alphabet. Therefore, the number of choices for the first position is 8, for the second position is 8, and for the third position is also 8. So the total number of choices for the letters is 8 * 8 * 8 = 512.
For the numbers, we are selecting 4 numbers from the digits 0 through 9 with no repeats. This can be calculated using the concept of combinations without repetition. The number of choices for the first number is 10 (as we have 10 digits to choose from), for the second number is 9 (as we have 9 remaining digits after selecting the first number), for the third number is 8 (as we have 8 remaining digits after selecting the first two numbers), and for the fourth number is 7 (as we have 7 remaining digits after selecting the first three numbers). So the total number of choices for the numbers is 10 * 9 * 8 * 7 = 5,040.
To find the total number of serial numbers that can be generated, we multiply the number of choices for the letters by the number of choices for the numbers: 512 * 5,040 = 2,582,080.
Therefore, a total of 2,582,080 serial numbers can be generated.