Choose or die

Number Theory Level 4

Calculate how many ways a family of n people can travel, under the following conditions:

- - There are two vehicles available. Each has capacity for n people and must carry at least one of them.

- - Both vehicles are similar or indistinguishable in appearance.

- - People are distinguished only to form two groups before boarding. After this moment, they are not distinguished in anything else, as, for example: to be the driver or not, seat location or any other aspect related to the vehicle and the trip in general.

2 n − 1 − 1 2^{n-1} - 1 2 n − 1 − 2 2^{n-1} - 2 n ( n − 1 ) 2 \frac {n(n-1)}2 2 n − 1 2^{n-1}

Jamil Silva by Jamil Silva , 52, Brazil

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