## Task 2 - 260522

Fritz has three red and three blue circular game tokens. No two of these six game tokens are the same size.

a) Fritz first lays only the three differently sized red game tokens next to each other on the table. Draw all possible arrangements of these three game tokens! How many arrangements are there in total?

b) Now Fritz wants to lay all six game tokens next to each other so that the colors of the game tokens always alternate.

How many possible arrangements of the game tokens are there in total? State the number and explain why there are exactly this number of possible arrangements!
a) There are exactly six such arrangements for the three red game tokens, and they are:
(1)
(4)


(2)
(5)

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0113.jpg?height=106&width=271&top_left_y=1826&top_left_x=938)
(3)
(6)

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0113.jpg?height=169&width=277&top_left_y=1823&top_left_x=1438)

b) Just like for the three red game tokens, there are exactly six possible arrangements for the three blue game tokens. Since the colors should alternate and each arrangement of the red tokens can combine with each arrangement of the blue tokens to form a new row, there are \(6 \cdot 6 = 36\) arrangements in total that start with a red game token, and equally many arrangements that start with a blue game token.

Therefore, there are 72 different arrangements of the required type for the three red and three blue game tokens.