Counting Prob (Mult. Choice)

Suppose that there are 6 available parking spaces in a parking lot. The spaces are labelled #1 through #6.

There are exactly 5 cars of 5 different colors: yellow, pink, white, gray, blue. The cars need to be placed in the parking spaces.

Three conditions need to be met:

-Pink car has to be placed in space #3.

-Blue car has to be placed in a space next to the parking space where yellow car is parked

-Gray car is not able to be placed in a space next to the parking space where white car is parked

1.) Suppose the yellow car is placed in parking space #1. Determine the number of parking arrangements there are for the 5 cars.

i.) 1

ii.) 2

iii.) 3

iv) 4

v) 5

2.) Which of the following has to be true of any parking situation:

i.) 1 of the cars is in space #2

ii.) 1 of the cars is in space #3

iii.) There exists an empty parking space next to the space where grey is parked

iv.) There exists an empty parking space next to the space where yellow is parked

v.) Either the blue OR the yellow car is parked in a parking spot next to space #3

3.) If the gray car is placed in space #2, none of the other cars are able to be parked in which parking spot?

i.) 1

ii.) 3

iii.) 4

iv.) 5

v.) 6

4.) The white car is able to be placed in any space, EXCEPT:

i.) 1

ii.) 2

iii.) 4

iv.) 5

v.) 6

5.) Assuming the yellow car is placed in slot #2, which of the following has to be true?

i.) No car is placed in space #5

ii.) Gray car is located in space #6.

iii.) Blue car is in a space next to the space where the white car is placed

iv.) White car is in a space next to the space where the pink are is placed

v.) Gray car is parked in a space next to the space where the blue car is placed