Question

If we create a 4 digit pin number using only the digits {0,1,2,3,4},

how many unique 4 digit pin numbers can we make?

Answer 1

Total number of 4 digit pins possible = 5 * 4 * 3 * 2 = 120   

Answer 2

Problem Statement:
We need to determine how many unique 4-digit PIN numbers can be created using only the digits {0, 1, 2, 3, 4}.

Key Observations:

1. Digits Allowed: The digits available are 0, 1, 2, 3, 4. This gives us 5 possible choices for each digit in the PIN.

2. 
   

3. PIN Length: The PIN is 4 digits long.

4. Repetition: The problem does not restrict repetition, so digits can be repeated (e.g., 0000, 1111, etc., are allowed).

5. 
   

6. Leading Zeros: The problem allows the PIN to start with 0 (e.g., 0123), so it is a 4-digit sequence rather than a strict 4-digit number where the first digit cannot be 0.

7. 
   

Calculation:

• For each of the 4 positions in the PIN, there are 5 possible choices (0, 1, 2, 3, 4).

• Since the choices are independent, the total number of unique PINs is calculated by multiplying the number of choices for each digit:

  $$\text{Total PINs}=5\times 5\times 5\times 5=5^4$$$$\text{Total PINs}=625$$

Answer:
The number of unique 4-digit PIN numbers that can be created is $\boxed{{\displaystyle 625}}$