There is a group of 6 Persons. They Play a game in which each has to select a positive integer from 1 to 4.

Let \({ A }_{ n }\) is the event that n persons have selections of same number, And the value of \(P\left( { A }_{ 5 } \right) +P\left( { A }_{ 6 } \right) =\frac { p }{ q } \).

Then Find \(p+q\)

**Note**

\(P\left( K \right) \) Denotes the probability of Event \(K\).

\(GCD\left( p,q \right) =1\)

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