How's It Possible?

You have a set of 20 different objects.

Let \(S\) be the total number of ways in which you can select and permute any number of these objects.

Find the digit sum of \(S\).

Details and Assumptions

  • The digit sum of a number is the sum of its individual digits. For example, the digit sum of 121 is \( 1+2+1 = 4 \).
  • You can pick any number of objects, from 0 to 20.

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