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(a) How many cards are in a complete deck of Set?

(b) How many unique sets are there?

When three cards form a set, we can also count the number of attributes for which all three cards are the same. For example, in the set below, all three cards have the same color, and the same shape (but they have different numbers of shapes and different shading).



(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.

 Jan 5, 2021
 #1
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(a) 81, because \(3^4\)

 Jan 5, 2021
 #2
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i do aops TOO guest. stop trying to cheat your writing problem. btw the aops admins know when your cheating. ;)

 Jan 6, 2021
 #3
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Which part of the problem do you need help with?

 Jan 8, 2021

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