Subject: PROBIBILITY Name: ASHLEY
Who is asking: Student
Question: Suppose that I was going to use a table or spread sheet to list all the possible combinations. There are 4 columns in this table; model, interior color, exterior color and transmission. How many rows do I need in the table?
If the only choice was "model" then you would need 32 rows in the table.
If you now want to fill in the "interior color" column then each of the 32 models needs 8 rows, one for each interior color.
Hence to fill in the first two columns in your table you need 32*8 = 256 rows. I hope you can see the pattern now. To fill in the exterior color column each of the 256 rows needs to be repeated 8 times, one for each exterior color. Hence you need 265*8 = 2048 rows. Finally for the last column there are 2 choices of transmission and thus in total you need 2048*2 = 4096 rows. This is called the Fundamental Counting Principal the number of combinations will be:(Different models)*(different interior colors)* (different exterior colors)*(options for transmission) = 32*8*8*2 = 2^{12} = 4096
