How many quasars are there in the universe?
Estimates are around 50,000.
The known quasars are incredibly distant object over 10 billion light years away. There are more quasars than have been observed which are not as bright as the ones which have been observed. Estimates based on the density of galaxies come to about 50,000.
Quasars are the result of material falling into a supermassive black hole at the centre of a galaxy. It is thought that quasars can only form in young galaxies and when galaxies collide. The huge energy output requires a lot of material falling into the black holes. This makes quasars relatively short lived.
It is known that many galaxies, including our own, have a supermassive black hole at their centre. These galaxies could have been quasars in their youth.
As the known quasars are so distant, what we are seeing are young galaxies as they were billions of years ago. They will have stopped being quasars. New quasars may form when galaxies collide.
So, although there may be quite a few visible quasars, at the present time there will be very few or maybe none at all.