SOLUTION: A rectangular flag is divided into four triangles, labelled Left, Right, Top, and Bottom as shown. Each triangle is to be coloured one colour of red, white, blue, and green, and

Question 1082985: A rectangular flag is divided into four triangles, labelled Left,
Right, Top, and Bottom as shown. Each triangle is to be coloured
one colour of red, white, blue, and green, and purple so that no
two triangles that share an edge are the same colour. How many
different flags can be made.
A)180
B)200
C)220
D)240
E)260
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!


I assume that it's this way:



Case 1: All four triangles have different colors:

There are 5 colors to choose for the LEFT triangle.
There are then 4 colors remaining to choose for the RIGHT triangle.
There are then 3 colors remaining to choose for the TOP triangle.
There are then 2 colors remaining to choose for the BOTTOM triangle.

That's 5*4*3*2 = 5P4 = 120 ways for Case 1.

Case 2: the LEFT triangle and the RIGHT triangle are colored alike
but the TOP and BOTTOM triangles are colored different.

There are 5 colors to choose for the LEFT and RIGHT triangles.
There are then 4 colors remaining to choose for the TOP triangle.
There are then 3 colors remaining to choose for the BOTTOM triangle.

That's 5*4*3 = 5P3 = 60 ways for Case 2.

Case 3: the TOP triangle and the BOTTOM triangle are colored alike
but the RIGHT and LEFT triangles are colored different.

That's the same number as Case 2, or 60 ways.

Total for the three cases: 120+60+60 = 240 ways to color the flag.

Edwin

RELATED QUESTIONS
Write the equation of the line that you would follow to cut the square table cloth into... (answered by mananth)

The flag of Scotland is divided into four triangles by a diagonal white cross. It is the... (answered by fractalier)

The flag of Scottland is divided into four triangles by a white cross. It is the cross of (answered by fractalier)

A woman is standing on a hill looking at a flag pole known to be 36 feet tall. If she... (answered by ccs2011)

ok, so i have a sideways hourglass looking figure 2 triangles obviously. starting at the... (answered by Edwin McCravy)

Hello, I have a question that I am having a lot of trouble with. I'll give you the... (answered by solver91311)

Hello, I have a question that I am having a lot of trouble with. I'll give you the... (answered by oscargut,Fombitz)

Hello..my name is Christopher Bush. I have a very diffult problem that my teacher has... (answered by solver91311)

You are placing a mat around a 25 inch by 21 inch painting as shown. You want the mat to... (answered by xalmax)