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Question: If there was a mulligan given to someone, will that make them able to select all the 32 teams again?
Answer: This depends on what your settings is. If your pick setting is turned ON for "team re-use" then your members would be able to re-pick a team after they are revived by a mulligans.
If your "team re-use" is OFF, if a member picks the bears for an example and they are out, if they are provided a mulligans, they will not be able to re-pick the bears again.
I hope this helps!