Mathematics Q.3

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 $K$ .

• $GCD\left( p,q \right) =1$