What is so special about \( 111 \) ?

Discrete Mathematics Level 5

Consider a regular \(111\) sided polygon. We will get a decagon by joining any \(10\) points of this \(111\) sided polygon.

In this polygon, how many decagon can be formed such that they do not have any side common with the \(111\) sided polygon?

If the answer contains \(m\) digits and sum of all digits of the answer is \(n\), find \( m + n \).

\( \text{Details and Assumptions :} \)

\(\bullet\) Sum of digits means sum of every individual digits. For example, sum of digits in number \( 122453\) is \( 1+2+2+4+5+3 = 17 \)

\( \bullet\) You may use computational tools


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