How many keys in a Hybrid Cryptosystem?
So first, for each employee there is a public-private-key pair, which is $2n$.

For each session one symmetric key is created. Your solution assumes the communication partners initially agree on a symmetric key they both use in the communication with each other. 

Considering a session as a communication in just one direction, instead of $n*(n-1)/2$ symmetric keys, there would be $n*(n-1)$ symmetric keys, making a total of $2n + n*(n-1) = 30$ keys

Edit for clarification:

The initial question states "each employee communicated with all other employees once"

This could mean two things:

$A$ sends a message encrypted with $symkey_1$ to $B$
$B$ responds with a message also encrypted with $symkey_1$
So $A$ communicated once with $B$ and $B$ communicated once with $A$

Another interpretation:

$A$ sends a message encrypted with $symkey_1$ to $B$
Two days later, $B$ sends a message to $A$ encrypted with $symkey_2$
So $A$ communicated once with $B$ and $B$ communicated once with $A$

The second interpretation will create $n*(n-1)$ symmetric keys, while the first one created only $n*(n-1)/2$ symmetric keys