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.

Step-by-step explanation:

Event A:

You can also write this as:

Event B:

You can also write this as:

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)

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

none of these

step-by-step explanation:

23 + 34 add up to 57 so just inform the teacher of this really stupid mistake