When to use "of" for [the color of a hat]

I have made up the examples below. I have also indicated my friends'opinions in brackets.

(1a) What colour hat do you like? (correct)

(1b) What colour of a hat do you like? (incorrect)

(2a) How many different colours of hats do you have? (correct)

(2b) How many different colour hats do you have? (incorrect)

Most of my non-native English speaking friends think (1a) is correct because "of a hat" in (1b) is wordy and unnatural. They think (2b) is correct because you are emphasizing the range of colours for your hats.

I am not sure if my friends are right. Please help me. Thank you very much for your time and help.