Question

Joe's Bank has improved its temporary PIN security. Now customers are randomly assigned a 4-digit temporary PIN that uses the digits 5, 6, or 7. Any of these digits may be repeated. How many possible PINs are there? ​

Answer 1

To find the number of possible 4-digit PINs using the digits 5, 6, or 7, we calculate 3^4 (since there are 3 choices per digit and 4 digits), resulting in 81 possible PIN combinations.

Step-by-step explanation:

The question asks how many possible 4-digit temporary PINs there can be if the digits used are 5, 6, or 7, with repetition allowed. To calculate the number of possible PINs, we use the counting principle which states that if we have n choices for one decision, and m choices for another, then there are n x m choices for both decisions combined. Since each of the four positions in the PIN can be filled with any of the three digits (5, 6, or 7), we multiply the number of choices per position by itself for each position:

Number of choices per position = 3 (digits 5, 6, or 7)

Possible PINs = 3 choices/position * 3 choices/position * 3 choices/position * 3 choices/position = 3^4 = 81

Therefore, there are 81 possible 4-digit temporary PINs when using the digits 5, 6, or 7 with repetition allowed.