This kind of topic is permutation and combination.
Five people go downstairs, the event is completed, and each person has eight choices.
(1) Maximum 1 probability of people leaving each floor.
Considering that these five people will definitely go down between the eight floors (objective problem), and at most one person on each floor, that is, five people will go down on the fifth floor respectively, then choose five floors from the eight floors first? And these five people are different and need to be arranged?
(2)? The probability of at least two people leaving on the same floor.
(1) direct method: 5-person combination includes
( 1+ 1+ 1+ 1+ 1)(2+ 1+ 1+ 1)(2+2+ 1)(3+ 1+ 1)(3+2)(4+ 1)(5)
(1+1+1+1) does not meet the requirements.
(2+ 1+ 1) Choose two of the five people who are together first, and the remaining three people are all 1. The combination is fixed, and then four layers are selected from the eight layers. The people downstairs are different. What's the plan?
(2+2+ 1) First, choose two people from five people together, then choose two people from the remaining three, and the remaining 1 people form a fixed combination. , choose the floor?
(3+ 1+ 1) Similarly?
(3+2) Similarly?
(4+ 1) Similarly?
(5) Choose one of the eight floors?
② Indirect method: According to the combination of (1) and 5 people, event A 1 and event A2 are mutually exclusive events, so
P2= 1-P 1
(2) Only one floor has the probability of two people leaving. The qualified combination is (2+1+1+1) (3+2).