I forgot to add the number of attributes so I'm posting the question again with that fixed
In the card game Set, each card features a number of shapes, with four attributes:
Number: The number of shapes is 1, 2, or 3.
Color: Each shape is red, purple, or green.
Shape: Each shape is oval, diamond, or squiggle.
Shading: Each shape is hollow, shaded, or striped.
There is exactly one card for each possible combination of attributes.
In the game, several of the cards are dealt out, and the goal is to find a set. A set is formed by three cards, where for each attribute, either all three cards are the same, or all three cards are different. When three cards form a set, we can also count the number of attributes for which all three cards are the same.
(a) How many cards are in a complete deck of Set?
(b) How many unique sets are there?
(c) Find the number of sets where all three cards are the same for exactly 0 attributes.
(d) Find the number of sets where all three cards are the same for exactly 1 attribute.
(e) Find the number of sets where all three cards are the same for exactly 2 attributes.
(f) Find the number of sets where all three cards are the same for exactly 3 attributes.
