Question 1191918
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<pre>

{{{C[n]^3}}} = 20  means  {{{(n*(n-1)*(n-2))/(1*2*3)}}} = 20,


which implies  n*(n-1)*(n-2) = 120.


It means n = 6  (easy trial and error or easy reasoning);  


hence n! = 6! = 720.


<U>ANSWER</U>.  720 permutations.
</pre>

Solved.