Question

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

sets

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1. - / 1 points

in recent years, a state has issued license plates using a combination of two letters of the alphabet followed by two digits, followed by another two letters of the alphabet. how many different license plates can be issued using this configuration?

different plates

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Explanation:

Step1: Calculate serial number count

There are 26 letters in the alphabet, and 10000 four-digit numbers (from 0000 to 9999).
$26 \times 10000 = 260000$

Step2: Calculate license plate count

There are 26 options per letter, 10 options per digit. We have 2 + 2 = 4 letters and 2 digits.
$26^4 \times 10^2 = 456976 \times 100 = 45697600$

Answer:

1. 260000 sets
2. 45697600 different plates