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A flag is made of three horizontal strips of fabric, each of a solid color, either red, white, blue or green. If no two adjacent strips can be the same color, how many distinct flags are possible? These two flags are different.

Sorry, canot get picture, but it means that the order matters from top to bottom.

 

Guest Nov 12, 2018
 #1
avatar+14578 
+1

9 x 4 = 36?

ElectricPavlov  Nov 12, 2018
edited by Guest  Nov 12, 2018
 #2
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0

It has 3 strips...and order matters

Guest Nov 12, 2018
edited by Guest  Nov 12, 2018
 #3
avatar+14578 
0

rwb

rbw

rgw

rwg

rgb

rbg

rwr

rbr

rgr

 

wbg

wgb

wbr

wrb

wgr

wrg

wrw

wgw

wbw

 

etc for the other two colors.....    

9 x 4 = 36   is what I find 

  ( I added the two stripes of same color but not NEXT to each other).....Anyone else?

ElectricPavlov  Nov 12, 2018
 #4
avatar+92787 
0

Here's my best attempt

 

We have 4 ways to choose the "top" color

Then, 3 ways to choose the next color

Then, 2 ways to choose the "bottom" color

 

 

So......the total possible flags  are   4 x 3 x 2   =   24

 

Another way to see this is all the possible sets  we can make by permuting  any 3 colors from a set of 4 colors....ordering the colors in the sets from left to right [ corresponding to top to bottom ], we have

 

4P3   =  24

 

 

cool cool cool

CPhill  Nov 12, 2018
 #5
avatar+14578 
+1

That's what I did originally, but you can use the same color twice.....just not next to itself.....which adds 12 mre possibilities.

 

Wondering if it wouldn't be     4 choices for first color   3 choices for second color  3 choices for third color = 36 possibles.

ElectricPavlov  Nov 12, 2018
edited by Guest  Nov 12, 2018
edited by Guest  Nov 12, 2018
 #6
avatar+92787 
+1

Ah, yes....that makes sense  !!!!

 

So....in that case...we have

 

4 colors on the top

3 colors in the middle

3 colors on the bottom

 

 

4 x 3 x 3  =   36

 

And you are correct.....!!!!

 

 

cool cool cool

CPhill  Nov 12, 2018

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