A three-digit PIN is formed by choosing each of its three digits at random from 0 to 9, repetitions being allowed. What is the probability that all three digits are different?

There are $10^3=1000$ equally likely PINs. All three digits differ in $10\times 9\times 8=720$ of them, so the probability is 720/1000 = 18/25. The complement 7/25 = 280/1000 is the probability that some digit repeats. Answering 3/25 = 120/1000 counts the digit SETS, C(10,3), and forgets that 123 and 321 are different PINs, and 1/100 = 10/1000 is the probability that all three digits are the same.