permutations and combinations

I think this is an English understanding problem Solviet.

 

If a pink card is next to a green card it can mean in either order.  Either pink,green or green,pink

 

If I cared about the order I might say that the pink is to the left (or right) of green

 

Do you understand this ?

i think:

9 cards each of different colour. 9 cards include a pink and a green card. How many different arrangements do not include a pink card next to a green card?

 

9 diffrent cards can be in 9! = 362880 arrangment s

 

So let s calculate how many arrangment we have if the pink card is next to green card(let s bring them together like 1):

8! = 40320

 

9!-8! = 322560

You are almost right Solveit.

 

Bur when you glue them together they can be  pink green   OR  green pink

 

So I believe the answer is

 

9!-   2*8! 

 

9!-2*8! = 282240