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If we take one of the C's out of "ECONOMICS" and place it first, we
have the letters of "EONOMICS" left to write after the C. So the
number of arrangements of "EONOMICS" that we can place after the
first letter C is 8!/2! = 20160 arrangements. The 8 is because
"EONOMICS" has 8 letters and the 2 is because it contains two
indistinguishable O's.
Edwin