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Permutation and Combination Problem

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by sukhman » Tue Sep 10, 2013 12:52 am
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
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by fcabanski » Tue Sep 10, 2013 8:03 pm
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.
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