Pacman positions 120 how? AI course

Question

I'm pursuing an Artificial Intelligence course online and I don't understand how the state space is calculated. In the following PDF on page 3 slide 2 it says that the possible pacman positions are:

12x10 = 120

Why is it so? And how did we get to this number?

Actually this is an excerpt from an online course by UC Berkley on Edx and though it is not shown in this slide but while calculating the state space they do the following:

12 x 10 x 4

where 4 is for the four directions in which the pacman can face, also it was never told that the area is bigger or they are only showing a portion o it.

Answer 1

This is because there are:

• 10 columns: five with "pellets" in them, and five that are empty.
• 12 rows: six with "pellets" in them, and six that are empty.