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danielvnl

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If we have 6 colours - green, red, blue, yellow, pink and black - and we have to paint a flag with 4 stripes.
restrictions:
1- we will only use one time each colour
2- If we use the green and yellow, they must be together, side by side.

How many ways we can paint this flag ?
 
My answer

Excluding the green and yellow we have 4 colours so we have 4! = 24 different ways.

With green and yellow, we have (G,Y,)_,_ - 2!*4*3 = 24

Adding this two groups we have 48 ways to paint the flag.

I'm not sure.

What do you think??
 
I don't know if it's correct if I use

(G,Y,)_,_ = 2!*4*3 = 24
_,(G,Y,)_ = 4*2!*3 = 24
_,_,(G,Y) = 4*3*2! = 24

adding this three 24+24+24 =72, plus the 24 ways without (green and yellow) = 96 different ways.

this is my doubt.
 
danielvnl said:
Excluding the green and yellow we have 4 colours so we have 4! = 24 different ways. CORRECT

With green and yellow, we have (G,Y,)_,_ - 2!*4*3 = 24 INCORRECT

What do you think??
Click to expand...

I think that you need four cases:
1) Using neither Green nor Yellow. (you did that correctly)
2) Using Green but not Yellow.
3) Using Yellow but not Green. (2 & 3 will give the same number)
4) Using Green and Yellow.

Lets explore 4).
There are two ways to have them together: (GY) or (YG)
There are three places to place the pairs: (GY) __ __, __ (GY) __ , __ __ (GY).
There are (4)(3) ways to fill the two blanks.
 
Last edited:
OK, so for the case 4) Using Green and Yellow.

(G,Y,)_,_ = 2!*4*3 = 24
_,(G,Y,)_ = 4*2!*3 = 24
_,_,(G,Y) = 4*3*2! = 24

Haven't we 72 different ways?
2) Using Green but not Yellow.
3) Using Yellow but not Green.
Click to expand...


you can't do that, yellow and green can't appear alone.
 
oh, sorry, I think you're right with this four case.

so we have

2)24 = 1*4*3*2
3)24 = 1*4*3*2

4) I'm not sure. 72
 
Last edited:
danielvnl said:
OK, so for the case 4) Using Green and Yellow.
(G,Y,)_,_ = 2!*4*3 = 24
_,(G,Y,)_ = 4*2!*3 = 24
_,_,(G,Y) = 4*3*2! = 24
Haven't we 72 different ways? CORRECT!
Click to expand...

danielvnl said:
you can't do that, yellow and green can't appear alone.
Click to expand...
danielvnl said:
If we have 6 colours - green, red, blue, yellow, pink and black - and we have to paint a flag with 4 stripes.
restrictions:
2- If we use the green and yellow, they must be together, side by side.
How many ways we can paint this flag ?
Click to expand...
The problem does not say that,

It says if you use Green and Yellow then they must appear together. The English is quite clear there.
Using only one of them negates the implication.
If you wanted it to mean that then it should read:
"if you use Green or Yellow then both must appear and they must appear together".
 
Yes, you're right pka.

So what do you think.

1)24
2)24
3)24
4)72 = 144 different ways.

Am I right??
 
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