Derek must choose a 4 digit PIN. Each Digit can be chosen from 0 to 9. Derek does not want to reuse

[math_celebrity]

Derek must choose a 4 digit PIN. Each Digit can be chosen from 0 to 9. Derek does not want to reuse any digits. He also only wants an even number that begins with 5. How many possible PINS could he choose from?

1. First digit must begin with 5. So we have 1 choice
2. We subtract 1 possible digit from digit 3 to have 8 - 1 = 7 possible digits
3. This digit can be anything other than 5 and the even number in the next step. So we have 0-9 is 10 digits - 2 = 8 possible digits
4. Last digit must end in 0, 2, 4, 6, 8 to be even. So we have 5 choices

Our total choices from digits 1-4 are found by multiplying each possible digit choice:
1 * 7 * 8 * 5 = 280 possible PINS