Question 1205496
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NOTE: The way the problem is presented, "cars" and "autos are distinctly different modes of transportation.<br>
The two people who insist on going together in the same car have 2 cars to choose from.  Number of choices: 2.<br>
The remaining 12 people are divided as follows: 2 more in the same car as the first couple, 4 in the other car, 3 in one auto, and 3 in the other auto.  The number of ways of making those arrangements is<br>
{{{12!/((2!)(4!)(3!)(3!))=277200}}}<br>
The number of ways the 14 people can depart with the given conditions is then 2*277200 = 554400<br>
ANSWER: 554400<br>
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