Question

We will be playing several rounds of Set game. There are 81 cards in a deck. There are three options for each of the four attributes:

Color - red, purple, green; number-1,2,3; shape-oval, squiggle, diamond; shading-solid, striped, outlined.
Given that there are 4 attributes (color, number, shape and shading), 3 options for each attribute, and one card in the deck for every possibility,

a. Show that each card is a member of (1)(80)/2 Sets.

b. Show that there are (81)(40)/3 different Sets in the whole deck.

Answer 1