A television game show has 14 doors, of which the contestant must pick 3. Behind 3 of the doors are expensive​ cars, and behind the other 11 doors are consolation prizes. The contestant gets to keep the items behind the 3 doors she selects. Determine the probability that the contestant wins at least one car.   The probability is ______. (integer or a simplified​ fraction.)

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.CR: Chapter Review
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A television game show has 14 doors, of which the contestant must pick 3. Behind 3 of the doors are expensive​ cars, and behind the other 11 doors are consolation prizes. The contestant gets to keep the items behind the 3 doors she selects. Determine the probability that the contestant wins at least one car.

 

The probability is ______. (integer or a simplified​ fraction.)

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