Thread: 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

Just takes a little logic.

1. The yellow car is in space 1, the blue car has to be next to it, pink is in 3, so only 4, 5 and 6 are open.

If grey is in 4, then white is in 6. (1)
If grey is in 5, white cant be parked.
If grey is in 6, then whie is in 4. (2)

Answer is 2 ways.

2. One of the cars is always in space 3, the pink one.

3. None of the cars can be in the first spot, white can obviously, yellow cant because blue cant park, and blue cant because it wont be next to yellow.

4. White car cant be in space 5 or it will seperate blue and yellow.

5. Blue would be in 1, yellow in 2, pink in 3, and then refer back to the first question; no cars can be parked in spot 5.