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! .
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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