6. Anna has five circular discs, each of a different size. She decides to build a tower using three of her discs so that each disc in her tower is smaller than the disc below it. How many different towers could Anna construct?
A 5
B 6
C 8
D 10
E 15
Solution
D

Let the discs be numbered 1, 2, 3, 4 and 5 in increasing order of size. The possible towers using three discs that Anna can build are, with the first number on top and then going down the tower, $123,124,125,134,135,145,234,235,245$ and 345 . Therefore she can build 10 different towers.