SOLUTION: Find the number of ways in which 14 people can depart in 2 cars of capacity 4 and 2 autos of capacity 3, if two people insist on going in the same car. (internal arrangements to be

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Find the number of ways in which 14 people can depart in 2 cars of capacity 4 and 2 autos of capacity 3, if two people insist on going in the same car. (internal arrangements to be      Log On


   

Question 1205496: Find the number of ways in which 14 people can depart in 2 cars of capacity 4 and 2 autos of capacity 3, if two people insist on going in the same car. (internal arrangements to be ignored)
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


NOTE: The way the problem is presented, "cars" and "autos are distinctly different modes of transportation.

The two people who insist on going together in the same car have 2 cars to choose from. Number of choices: 2.

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

12%21%2F%28%282%21%29%284%21%29%283%21%29%283%21%29%29=277200

The number of ways the 14 people can depart with the given conditions is then 2*277200 = 554400

ANSWER: 554400

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