Expert: Paul Klarreich - 3/2/2006

Question
A large van is being used for a picnic. There will be 6 people riding in the van, and there are 6 seats in the van, one of which is the driver's seat. One of the people will have to drive. Only 2 of the people are licensed to drive the van. In how many different ways could the people seat themselves in the van so that they have a licensed driver?


I thought the answer was 72 because of 6*6*2 but apparently im missing a part

Answer
Hi, Kevin,

You wrote:
Subject:  Combination problem
Question:  A large van is being used for a picnic. There will be 6 people riding in the van, and there are 6 seats in the van,

>> You call that a large van?  My minivan seats more.

one of which is the driver's seat. One of the people will have to drive.

>> Good idea.

Only 2 of the people are licensed to drive the van. In how many different ways could the people seat themselves in the van so that they have a licensed driver?

I thought the answer was 72 because of 6*6*2 but apparently im missing a part

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You choose the driver in two ways.  That leaves five people to put in the five remaining seats, and there are 5! ways to do that.

I think the answer is the product,  5! * 2 = 5 4 3 2 1 2 = 240