Hello, wvlilgurl!

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".

Theonly waythat two or less people get off on all the floors

. . is iftwo people get off on each floor.

This can happen in ways.

Hence: .

Therefore: .

I'll letyoureduce 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-threeget off on one the floors, right?will

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 thesamefloor.

Then we have three "families": .

. . They can get off in: ways.

Hence, the two children get off ondifferentfloors in: ways.

Therefore: .