Maximum Occupancy in Private Single Family Home

My question involves landlord-tenant law in the State of: New York and/or Islip Township

I saw a rental listing today in the town of Islip, in Bayshore NY. It was a 2200 sq ft two story house with three bedrooms and 2 baths. It was listed on Facebook. The person listing it said "Max 4 people". I have looked around the internet (and on e360 I think it is) and I haven't found anything specifically relating to private single family houses, only apartments or public housing in regards to how many people, or if someone is allowed to put a lower cap on the maximum.

Someone asked a friend of theirs who is in real estate and h/she said the following:
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She said that since it is a single unit, the landlord ABSOLUTELY has the right to restrict the number of people he rents to, as long as he doesn't use a rental company or real estate agent to list the property for him. The laws are different for apartment houses, complexes, and for properties that contain greater than 6 units. A property that is 4 units or less MAY still be considered, "owner/occupant", and the laws are slightly different then, as well. And, a single family residence does not fall under New York State Rent Stabilization Laws, which governs properties containing 6 units or more.
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So, in a nutshell can the landlord legally deny a family of 5 for the above mentioned house? Does this fall under discrimination? Or any other law?

thanks!

Maximum Occupancy in Private Single Family Home