A) The number of cards that are in a complete deck of Set is; 81
B) The number of unique sets are; 36
<h3>How to find the combination of a set of cards?</h3>
a) We are given;
Number of shapes = 1, 2 or 3
Colour = Red, Purple or Green
Shape = Oval, Diamond or Squiggle
Shading = Hollow, Shaded or Striped
Now, since a set is formed by all 3 cards, then we can say that;
Number of cards in a complete deck of set = 3⁴ = 81 cards
(b) Let us first find all sets = 3² * 4 * 3 = 108.
Thus;
Unique sets = 108/3
= 36 unique sets.
(c) There are 3 ways to choose the number of the cards from the given order.
For the second one, there 2 choices, and then there is only 1 choice. Thus; Number of ways to choose the numbers = 3 * 2 * 1 = 6.
For the other attributes;
Number of ways = 6 * 6 * 24 *6 ways.
Now, since the order of cards doesn't matter in a set, then the number of sets where all three cards are the same for exactly 0 attributes is;
(6 * 6 * 24 *6)/3! = 864 sets
(d) If all the colors are the same, then;
Number of sets = 6 * 24 * 6/3! = 144 sets.
If all the numbers are the same, then there are 144 sets which is also same for shapes and shading. Thus;
The number of sets where all three cards are the same for exactly 1 attribute is; 4 * 144 = 576
(e) There are C(4, 2) = 6 ways of choosing two attributes.
For each of the two attributes, there are 3 options.
For the other two attributes, there are 3 ways of assigning the choices. Thus, number of sets = 6*3*3*3*3 = 486 sets.
(f) There are C(4,3) = 4 ways of choosing which attributes are the same. There are 3*3*4 = 36 ways to assign which is which for each of these three attributes, and there are 4 ways to assign the choices for the fourth attribute. Thus;
The number of sets where all three cards are the same for exactly 3 attributes = 4*36*4 = 576 sets.
Read more about Card combinations at; brainly.com/question/27447394
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