Subject: PROBIBILITY

Name: ASHLEY

Who is asking: Student
Level: Middle

Question:
THE CAR DEALERSHIP IN TOWN OFFERS 32 DIFFERENT MODELS OF VIHICLES.EACH MODEL HAS A CHOICE OF EIGHT INTERIOR COLORS,EIGHT EXTERIOR COLORS,AND ALSO THE OPTION OF AUTOMATIC OR MANUAL TRANSMISSION. HOW MANY COMBINATIONS ARE POSSIBLE? (HINT:YOU HAVE TO USE MULTIPLICATION)

Hi Ashley,

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.

modelinteriorexteriortransmission
model 1
model 2
.
.
model 32

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.

modelinteriorexteriortransmission
model 1 color 1
model 1 color 2
model 1 .
model 1 .
model 1 color 8
model 2 color 1
model 2 color 2
. .
. .
model 32 color 8

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 = 212 = 4096

Penny and Andrei
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