Sheet # 4/The Summer Olympics-Critical Thinking

Name: _____________________ Date_____________

The Olympic symbol consists of five interlacing rings of the color blue, yellow, black, green and red. It represents the union of the five continents (Europe, Asia, Africa, Australia and America). How many different ways can you arrange the five rings to have the same shape?

Answer for sheet # 4:

The answer is 120 ( 5 rings x 4 x 3 x 2 x 1 = 120)

Let us start with two rings ( red and blue)

There are two combinations

red blue
blue red

Now take three rings (red, blue, green)

Now you can arrange the three rings 6 ways

red blue green
red green blue
blue red green
blue green red
green red blue
green blue red

6 combinations ( 3 rings x 2 x 1 = 6)

Using the above logic, you can arrange 5 rings in 120 ways ( 5 x 4 x 3 x 2 x 1 = 120)