SOLUTION: For an automobile rally, drivers draw lots for their starting positions. What is the probability that, out of the 25 drivers, three of the four Smith brothers will be chosen to sta

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Question 1178242: For an automobile rally, drivers draw lots for their starting positions. What is the probability that, out of the 25 drivers, three of the four Smith brothers will be chosen to start in the first three positions? Justify your solution.
Answer by ikleyn(52824) About Me  (Show Source):
You can put this solution on YOUR website!
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    P = C%5B4%5D%5E3%2FC%5B25%5D%5E4.


The denominator  C%5B25%5D%5E3 = %2825%2A24%2A23%29%2F%281%2A2%2A3%29 = 2300  is the number of all possible triples of 25 drivers.


It is the total set of events.



The numerator  C%5B4%5D%5E3 = 4 is the number of favorable triples of the four Smith brothers.


It is the set of all favorable triples.



The ratio  P = favorable%2Ftotal = 4%2F2300 = 1%2F575 = 0.001739 is the probability under the question.    ANSWER


Solved, answered and explained.


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In the other form, this probability is     P = %284%2F25%29%2A%283%2F24%29%2A%282%2F23%29 = 0.001739,   which is the same number/answer.


The last formula may seem to be more self-explanatory to you . . .