1. The problem asks for the number of 4-digit PIN codes with no repetition of numbers. 2. To find the number of possible 4-digit PIN codes with no repeated digits, we use permutations because order matters and digits cannot repeat. 3. The formula for permutations of $n$ objects taken $r$ at a time is: $$P(n,r) = \frac{n!}{(n-r)!}$$ where $n$ is the total number of digits to choose from (0 to 9, so $n=10$), and $r$ is the number of digits in the PIN (4). 4. Calculate the number of permutations: $$P(10,4) = \frac{10!}{(10-4)!} = \frac{10!}{6!} = 10 \times 9 \times 8 \times 7 = 5040$$ 5. Therefore, there are 5040 possible 4-digit PIN codes with no repeated digits. 6. The importance of knowing the number of ways to arrange things includes: - It helps in understanding the security strength of PIN codes. - It aids in calculating probabilities in various scenarios. - It is useful in organizing and planning arrangements efficiently. 7. The importance of a PIN code is: - It protects your phone from unauthorized access. - It ensures your personal data remains secure.