A man wants to visit at least two of the four cities A, B, C and D. How many travel itineraries can he make? All cities are connected to one another. Answer 4P2 + 4P3 + 4P4
At least two means visiting 2 or 3 or 4 cities. The order matters, because going to New York then Los Angeles, for example, is a different itinerary than going to Los Angeles then New York. Since order matters, use permutations.
Visiting 2 cities out of 4, when order matters, is 4P2.
Visiting 3 out of 4, order matters, is 4P3.
Visiting 4 out of 4, order matters, is 4P4.
Add them together to get the total number of itineraries: 4P2 + 4P3 + 4P4.
This is a simple problem. The solution is the definition of permutations.
