Permutation: Number of ways 4 cars could park

Question

I came across this question in my Algebra textbook:

Find the number of ways 4 cars could park right next to each other if the parking slots were:

a) in a straight row

b) in a circular form

knowing that there are 10 parking slots available in total.

Here is my approach to solving the question:

a) There are 7 ways to begin with. Multiplying 7*4P4 or simply 7*4! should then be the answer.

b) I am not sure whether the point of beginning makes any difference here as the slots are circular so my guess is that the answer should be 1P1*3P3 or 3!

Am I right? Thanks!

Answer 1

(a) Good work, your answer is correct.

(b) There are two possible interpretations of the problem; as you indicate, it's unclear whether or not the point of beginning matters, or in other words, whether any rotation of the cars around circle is the same.

• If the point of beginning does not matter, your answer of $3!$ is exactly right.

• If the point of beginning does matter, you would proceed similarly to (a), except there are $10$ possible points of beginning instead of $7$.