Question

Why the only third estate paid tax but the second estate could not paid tax

Answer 1

Because,the second estate were nobles and they are the administrative part of the country so due to that advantage they enjoyed the privileges like exemption from paying tax ,collecting the tax from the third estate etc.
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Answer 2

Answer:

Second and first estates had special powers or rights. They were nobles and Clergy's who enjoy privelages under their birth but the 3rd estate do not have such privelages from birth. So, they are the only estate who have to pay the tax

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