Dustin has a set of 180 distinct blocks. Each of these blocks
is made of either wood or plastic and comes in one of three sizes
(small, medium, large), five colors (red, white, blue, yellow,
green), and six shapes (triangular, square, rectangular, hexagonal,
octagonal, circular). How many of the blocks in this set
a) the small red wooden square block in exactly one way?
(For example, the small red plastic square block is one such
b) the large blue plastic hexagonal block in exactly two
ways? (For example, the small red plastic hexagonal block
is one such block.)
listing the differences for part a) was simple but part b) I am unsure of
Stacey Warren - Expert brainly.com
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This question is interesting. So there are 4 sets of characteristics: Material, Size, Color, Shape.
a) Small Red Wooden Square
not Small = Medium & Large., so 2/3 of the blocks;
not Red = the other 4 colors, so 4/5 of the blocks;
not Wooden = Plastic, so 1/2 of the blocks;
not Square = the other 5 shapes, so 5/6 of the blocks.
This is where I'm stuck. So we pick the largest fraction now? 5/6? (5/6) * 180 = ??
no, you would add all them up, not as fractions. there are 2 differences in size, 4 in color, 1 in material, and 5 in shapes. Thats 12 varatations and what I did was just list them out.
changing the shape:
small, red, wood, triangular
small, red, wood, rectangular
small, red, wood, hexagonal
small, red, wood, octagonal
small, red, wood, circular
changing the material:
small, red, plastic, square
changing the color:
small, white, wood, square
small, blue, wood, square
small, yellow, wood, square
small, green, wood, square
changing the size:
medium, red, wood, square
large, red, wood, square
This would not be as simple for part B though and I am unsure of where to start with that one.
b) Large Blue Plastic Hexagonal
And different in exactly two ways
so the other blocks could be:
-Large Blue but not Plastic and not Hex
-Large Plastic but not not Blue and not Hex
-Large Hex but not Blue and not Plastic
-Blue Plastic but not Large and not Hex
-Blue Hex but not Large and not Plastic
-Plastic Hex but not Large and not Blue
Is that all? Did I miss a case?
There must be a better way to do this...
Not the answer you are looking for? Search for more explanations.
OK so how many blocks are there in each variation for a)?
There are 12 variations with only one thing not in common from the original block for A
Using your list i took the number of possible differences for each and multiplied them. Once done for every catagory just used the rule of sum and I believe thats the answer but not positive.
Large Blue but not Plastic and not Hex: 1*5 = 5
Large Plastic but not Blue and not Hex: 4*5 = 20
Large Hex but not Blue and not Plastic: 4*1 = 4
Blue Plastic but not Large and not Hex: 2*5 = 10
Blue Hex but not Large and not Plastic: 2*1 = 2
Plastic Hex but not Large and not Blue: 2*4 = 8
Total of 49 blocks
OK, two Materials, three Sizes, five Colors and six Shapes.
2*3*5*6 = 180
So isn't there only 1 block per variation because there are 180 blocks?
Not to sure where you are going with that. It it isnt hex then there are 5 different options it could be instead and so on for the other characteristics.
3 sizes 5 colors 6 shapes 2 materials
s r t w
m w s p
l b r
3*5*6*2 = 10*18 = 180 different elements
-l, -b, p, h
-l, b, -p, h
-l, b, p, -h
l, -b, -p, h
l, -b, p, -h
l, b, -p, -h
are all the sets that differ l,b,p,h by exactly 2 properties
the letters that are "positive" in my write up are the common properties and equate to 1 (since they are the only property that spot can have); the others reduce by one since they have to differ by 1.