Question

2
select the correct answer.
how many ways can a password be created with 3 lowercase letters and 1 numeric digit, if letters can be used more than once?
a. 175,760
b. 14,950
c. 17,576
d. 358,800

Explanation:

Step1: Determine choices for letters

There are 26 lowercase letters, and each of the 3 letter positions has 26 choices (since letters can repeat). So for the 3 letters, the number of ways is $26\times26\times26 = 26^3$.

Step2: Determine choices for digit

There are 10 numeric digits (0 - 9), so the digit position has 10 choices.

Step3: Calculate total number of passwords

By the multiplication principle, multiply the number of ways for letters and the number of ways for the digit. So total ways = $26^3\times10$.
Calculate $26^3 = 26\times26\times26 = 17576$, then $17576\times10 = 175760$.

Answer:

A. 175,760