SOLUTION: the word "veracious" In how many ways can you arrange the 9 letters such that V and C are never adjacent to each other?

Question 789225: the word "veracious"
In how many ways can you arrange the 9 letters such that V and C are never adjacent to each other?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
There are 9! = 9*8*7*6*5*4*3*2*1 = 362,880 different ways to arrange all 9 letters.

If we think of V and C as one letter, call it z, then we have the "word" "zeraious" and there are 8! = 8*7*6*5*4*3*2*1 = 40,320 ways to arrange these letters. Double this amount to account for CV to get 2*40,320 = 80,640

So there are 80,640 words where V and C are together (either as VC or CV)

So there are 362,880 - 80,640 = 282,240 different words where V and C are never adjacent to each other.
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