Three people step into a building that has 4 lifts. Each person picks a lift at random, independently of the others. What is the probability that at least two of them pick the same lift?

Count the opposite event. The three people choose three different lifts in $4\times 3\times 2=24$ of the $4^3=64$ equally likely triples, a probability of 24/64 = 3/8. Hence P(at least two share a lift) = 1 − 3/8 = 5/8. Answering 3/8 is the forgotten complement, and 1/16 counts only the case where all three choose one particular lift.