Good question I've heard more cases of 'types of Xs' in speakers of Am Eng, and more of the singular X in British Eng. I've heard more or less shrill defences of either usage and its alleged 'logic'. I shall listen and learn ...
(In the meantime, my practice is to avoid this format - 'I don't know which types of choice to make' => 'One type of choice seems much the same as another.')
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