There are several different types of happiness.
There are many different kinds of government.
There are many types of golf balls.
Since we are talking about different types of happiness would you need to make it plural (happinesses). I know it’s an uncountable noun, but it’s confusing. My question for the second is pretty much the same as I want to know if it should be government or governments. And the third sentence I know is correct, but it’s made plural unlike the other ones.