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I'm interested in asking a survey question ("How did you hear about us?") to people that visit a website. I'd like to have it be multiple choice, but since there are many different sources (referral, tv ad, social media, there are at least 8 more) and I suspect the answer quality will be worse if someone is confronted with all possible options, I'm wondering a few things:

a) the optimal number of possible answers for the question

b) if presenting a random set of N possible answers for each person is a good way to get full coverage for the set of sources

c) if b) is fine, how many people we need to survey to get reliable estimates.

My background's in machine learning and NLP, so I'm not too well versed in survey sampling. Thought I'd post it here to get some ideas. Thanks!

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