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?

[asy]
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));
[/asy]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
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?

[asy]
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));
[/asy]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
24
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?

[asy]
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));
[/asy]
train