Pin the tail on the factorial

You are told that the last fourteen digits of \(33!\) (from the right) are \[ \overline{94401abc000000}, \] where \(a, b\) and \(c\) are digits. What is the value of \(\overline{abc} \)?

Details and Assumptions:

  • \( \overline{abc}\) means \( 100a + 10b + 1c\), as opposed to \( a \times b \times c\). As an explicit example, for \(a=2, b=3, c=4\), \(\overline{abc} = 234\) and not \( 2 \times 3 \times 4 = 24\).

  • The last 3 digits of the number \(1023\) are \(023\).

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