There are 17 different vehicle models available at the deale

There are 17 different vehicle models available at the dealership. Oddly, each family living on Maple Street bought one of these vehicles. There are just enough families on Maple Street so you can be absolutely sure that 5 families all have the same model. How many families are there on Maple Street?

This is a discrete mathematics problem, please help.

Solution

If there are 17*4 =68 families then we can give 4 family a car of one model and since there are 17 models so all families will ahve a car and no 5 families will have the same model.

But one more family and it has to have a model already purchased by 4 of the families. So at least 5 families have the same model. So there must be 69 families as this is the minimum number to ensure 5 families ahve the same model.