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There are 8 streets to be named after 8 tree types. Ash, Birch, Elm, Fir, Maple, Pine, Spruce, and Willow.  A city planner randomly selects the street names from the list of 8 tree types.  Compute the probability of each of the following events.

Event A: The first three streets are Ash, Elm, and Pine, without regard to order.

Event B: The first street is Willow, followed by Spruce and then Fir.

 Mar 1, 2020
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A) \(\text{There are 3! orderings of the first 3 streets and then 5! ways to arrange the rest of them}\\ \text{There are a total of 8! orderings of the streets}\\ p = \dfrac{3!5!}{8!} = \dfrac{6}{336} = \dfrac{1}{56}\)

 

B) \(\text{Now there is only 1 ordering of the first 3 streets, and then 5! orderings of the rest}\\ p = \dfrac{5!}{8!} = \dfrac{1}{336}\)

.
 Mar 1, 2020

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