A building has 10 doors and 5 persons will enter this building. What is the probability that the first four persons will enter the building through 4 different doors and the fifth person will use one of these 4 doors?
The first person can chooses any of the 10 doors. The second person can choose any of the 9 remaining doors, the third 8 doors and the fourth 7 doors. The fifth person enter through any of the those four doors. There are, then 10(9)(8)(7)(4) ways the five people can enter. Without any restrictions there are ways for 5 people to enter through 10 doors. The probability of the given situation is . Since , that is the same as your answer.