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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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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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