We are playing the game set with a deck of cards. given that there are 4 attributes (color, number, shape, and shading), 3 options for each attribute, there are 81 cards in the deck. a set is three cards where each feature, when looked at individually, is either all the same or all different. each card contains four features: color (red, purple or green), shape (oval, squiggle or diamond), number (one, two or three) and shading (solid, striped or outlined).

use counting techniques to answer the following.

(a). how many sets is each card a member of?

(b). how many different sets are there in the deck?

(c). if you deal 10 cards from the deck, can you be sure that there will be at least one set among them? prove your claim.