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. Write your answers as fractions in simplest form.

[tex]\dfrac{\text{Ash, Elm, or Pine}}{\text{All 8 tree types}}\times \dfrac{\text{(Ash, Elm, or Pine) - 1}}{\text{remaining 7 tree types}}\times \dfrac{\text{(Ash, Elm, or Pine) - 2}}{\text{remaining 7 tree types}}\\\\\\\dfrac{3}{8}\times \dfrac{2}{7}\times \dfrac{1}{6}\times \dfrac{5}{5}\quad =\quad \large\boxed{\dfrac{1}{56}}[/tex]

You can also write this as:

[tex]\dfrac{1}{_8C_3}\ = \ \dfrac{1}{56}\\\\\\or\\\\\\\dfrac{8!}{3!(8-3)!}\ = \ \dfrac{1}{56}[/tex]

Event B:

[tex]\dfrac{\text{Willow}}{\text{All 8 tree types}}\times \dfrac{\text{Spruce}}{\text{remaining 7 tree types}}\times \dfrac{\text{Fir}}{\text{remaining 6 tree types}}\\\\\\\\\dfrac{1}{8}\times \dfrac{1}{7}\times \dfrac{1}{6}\quad = \quad \large\boxed{\dfrac{1}{336}}[/tex]

You can also write this as:

[tex]\dfrac{1}{_8P_3}\ = \ \dfrac{1}{336}\\\\\\or\\\\\\\dfrac{8!}{(8-3)!}\ = \ \dfrac{1}{336}\\[/tex]

Notes:

In Event A, order did NOT matter so it was a COMBINATION (C)

In Event B, order DID matter so it was a PERMUTATION (P)