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Could someone please help me? I've tried this problem by myself but it never seems to work out. Thanks!

 
 Jun 7, 2021
 #1
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(b) There are 108/3 = 36 unique sets.

(c) For the first card, there are 3 ways to choose the number.  For the second, there 2 choices, and then there is only 1 choice.  So there are 3*2*1 = 6 ways that the numbers can be chosen.  Doing this for the other attributes, we get 6*6*24*6 ways.  But the order of cards doesn't matter in a set, so we divide by 3!: 6*6*24*6/3! = 864.  So there are 864 sets for part (c).

(d) The cards can have the same number, color, shape, or shading.  If all the colors are the same, then there are 6*24*6/3! = 144 sets.  If all the numbers are the same, then there are 144 sets.  We get the same number for shape and shading, so there are 4*144 = 576 sets for part (d).

(e) We need to choose two of the attributes.  There are C(4,2) = 6 ways of choosing two attributes.  For each of these two attributes, there are 3 options.  For the other two attributes, there are 3 ways of assigning the choices, so there are 6*3*3*3*3 = 486 sets for part (e)

(f) First we choose which attributes are the same.  There are C(4,3) = 4 ways of choosing which attributes are the same.  There are then 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, so there are 4*36*4 = 576 sets for part (f).

 
 Jun 7, 2021
 #2
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Are you happy with guest's answers?   (Perhaps you have a final answer sheet)

 

If you are then at least express some gratitude.

 

If not, then say so,  people are happy to interact with question askers that are genuinely trying to learn.

 
 Jun 8, 2021
 #3
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Thank you so much! This really helped me out!

 
 Jun 8, 2021
 #4
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Also, could you please help me out with part a? Is it 3^4?

 
 Jun 8, 2021
 #5
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Is there more to this question?

The pic comes AFTER part b  So what are the instructions for part a and part b.

Nowhere does it say that you can only have 3 objects on a card.  Maybe you can have 20 objects or 50 etc

So could you determine the number of possible combinations?

 

Guest made assumptions when answering, and maybe those assumptions were as intended but mathematics should be precise and this question is pitiful.

 
 Jun 8, 2021
 #6
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Oh, sorry!

 

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 solid.

There is exactly one card for each possible combination of attributes.

 

Is this better?

 
 Jun 8, 2021
 #7
avatar+113567 
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Of course,

How can anyone answer a question if you only include half the question?

This whole question has been a total waste of everyone's time. Including yours.

 
Melody  Jun 9, 2021

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