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The letters C, O, U, N and T are randomly placed around a circle. One such arrangement is shown here. If we always start with the C and continue to read the rest of the letters in order clockwise, in how many different orders can the letters appear?

 draw(circle((0,0),1),dashed); label("U",dir(90)); label("C",dir(90+360/5)); label("O",dir(90+2*360/5)); label("N",dir(90+3*360/5)); label("T",dir(90+4*360/5));

 Mar 29, 2015

Best Answer 

 #1
avatar+118724 
+10

4! ways 

 Mar 29, 2015
 #1
avatar+118724 
+10
Best Answer

4! ways 

Melody Mar 29, 2015
 #2
avatar+130518 
+5

Well since "C" is in a given position, and we're going in a clock-wise manner, we have 4 ways to choose the next letter, 3 ways to choose the letter after that, etc.

So  4 x 3 x 2 x 1= 4!  = 24 arrangements

 

  

 Mar 29, 2015

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