apt is a command line interface for Ubuntu package manager.

Apt List Installed Ubuntu Packages

To list all the installed packages, use following command...

sudo apt list --installed

To count, you can just pipe the above output to wc -l

sudo apt list --installed | wc -l
781

Of course you can pipe to any Unix command. Examples...

sudo apt list --installed | less
sudo apt list --installed | egrep <pkg_name>

Dpkg-query List Installed Ubuntu Packages

dpkg-query is old way of querying installed packages on Ubuntu. The command is still available on newer versions too.

To list installed packages, run following command...

 sudo dpkg-query -l

And the pipe commands can be used to narrow down the results....

 sudo dpkg-query -l | less
 sudo dpkg-query -l | egrep <pkg_name>