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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.

A) 24 B) 6 C) 60 D) 12 E) None of the above

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elijahjoseph1

Answer: C) 60

Step-by-step explanation:

"At least 2" simply means 2 or more.

2 cities can be selected from 4 cities in 4C2 ways and these two cities, let's say A and B would have two distinct itineraries AB and BA.

Mathematically, that can be done either in 4C2*2! or 4P2 ways = 12.

Also, 3 cities in 4C3*3! or 4P3 ways = 24; that is, 4 cities in 4C4*4! or 4P4 ways = 24.

Total 12+24+24=60 ways.

The correct option is C

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