SOLUTION: Nine cards, all in a different colour, 3 cards are selected from the 9 cards and arranged in a line. How many different possible arrangements of 3 selected cards do not have the pi

Question 1175421: Nine cards, all in a different colour, 3 cards are selected from the 9 cards and arranged in a line. How many different possible arrangements of 3 selected cards do not have the pink card next to the green card?
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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Nine cards, all in a different colour, 3 cards are selected from the 9 cards and arranged in a line.
How many different possible arrangements of 3 selected cards do not have the pink card next to the green card?
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In all, there are 9*8*7 = 504  different possible arrangements of 9 different object 
(colored cards, in this case), taken 3 at a time.



From this number, we should subtract those unwanted arrangements, where pink is next to green card.



The number of such unwanted arrangements is  2*2*7 = 28 (there are 2 possible positions for such pair of cards 
in the short line of 3 positions;  there are 2 ways to order these 2 card (pink/green or green/pink) 
and there are 7 ways to supplement these two cards by the third card.



So, the final answer is: the number of ways is  9*8*7 - 2*2*7 = 504 - 28 = 476.

Solved.

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