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In how many ways can we distribute five people in a car if exactly two of them are can drive?

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Welcome to Math StackExchange. I answered your question making the best sense of it. Please use the "edit" option to add to your question explaining what you tried. Also, use the homework tag if the question belongs to your homework. – Parth Kohli Jan 8 '13 at 11:07

We can have two people at the driver's seat, and others can have a seat wherever they want.

  • For the driver's seat (S1), there are two possibilities.
  • For the next seat (we'll label it as S2), there are $4$ possibilities.
  • For the next seat (S3), there are $3$ possibilities.
  • For the next seat (S4), there are $2$ possibilities.
  • For the next seat (S5), there is only one possibility.

Simply multiply the possibilities for S1, S2, S3, S4 and S5 which yields $2\cdot 4 \cdot 3\cdot 2 \cdot 1$.

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I don't think every one can drive a taxi even though they are good drivers.. (Just for fun not related to your answer or question). :) – Ram Jan 8 '13 at 10:58

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