1) Is dancing in a wedding where males and females are segregated permissible?
2) What about the dancing of the couple which they call the “first dance”. I mean dancing when there is no haram music being played

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According to S. Sistani, dancing is not permissable, neither for males among males, nor for females among females.
It is only allowed for the husband and wife, when they are alone. For sure, there should not be haram music.