1. In early history, when no houses had running water,
most people used outdoor pit privies. Only very rich people
could reserve one indoor room for this purpose. They kept
it closed and it was small, thus called a closet.
2. Piped water supply to private houses provided the basis
for the 19th century flush toilet. Someone with a flushing
water supply to his closet called it a water closet = WC,
the common euphemism in Britain (and France. But
"lavatory" and "toilet" are euphemisms as well.)
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