Question

part one - multiple choice (circle the best answer)

1. a library code is 3 digits (0 - 9) followed by two letters. how many codes are possible?

a. 468 b. 492,804 c. 527,000 d. 676,000

Explanation:

Step1: Calculate the number of digit combinations

Each digit has 10 possibilities (0 - 9). For 3 digits, by the multiplication principle, the number of combinations is \(10\times10\times10=10^{3}\).

Step2: Calculate the number of letter combinations

There are 26 letters in the alphabet. For 2 letters, the number of combinations is \(26\times26 = 26^{2}\).

Step3: Calculate the total number of codes

By the multiplication principle (since the digit - part and letter - part are independent), the total number of codes is \(10^{3}\times26^{2}\).

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Answer:

D. 676,000