Hey there

As I have searched there is no information particularly related to how many colleges we can select. I think you will get colleges according to your scores.  However Mentioned below are the number of colleges participating in JOSAA counselling:

• There are total 170 participating colleges.
• Out of which 23 are Indian Institutes of Technology and 25 IIITS, 31 NITs and 28 GFTIS.

For more:

https://www.google.com/url?sa=t&source=web&rct=j&url=https://josaa.nic.in/WebInfo/Page/Page%3FPageId%3D1%26LangId%3DP&ved=2ahUKEwi66J2__LDzAhXVyzgGHWkXBH0QFnoECAkQAg&usg=AOvVaw17Um84VEIIZd2qtERxS-IW