Each of the 10 people have a choice of 5 floors.Ten people get on an elevator on the first floor of a six-story building.
Assume that each of the 10 people get off at random at any one of the five upper floors.
a) What is the probability that 3 or more people get off at least one floor?
. . There are possible outcomes.
The opposite of "three or more people" is "two or less people".
The only way that two or less people get off on all the floors
. . is if two people get off on each floor.
This can happen in ways.
I'll let you reduce the fraction . . .
The families are: .b) Assume that the 10 people are actually 4 couples and 2 of the couples have 1 child each.
Assume also that families get off at the same floor.
What is the probability that 3 or more people get off at least one or more floors?
A family-of-three will get off on one the floors, right?
The probability is: 1.00 = 100%.
There are four families: .c) Again assume the 10 people are 4 couples and 2 children.
What is the probability that the 2 children get off on different floors?
. . They can get off in ways.
Suppose the two children get off on the same floor.
Then we have three "families": .
. . They can get off in: ways.
Hence, the two children get off on different floors in: ways.