For what it's worth, the article formalises "one 6 from 6 dice" as "at least one 6", and similarly for the other events, which throws off your probability (whic

For what it's worth, the article formalises "one 6 from 6 dice" as "at least one 6", and similarly for the other events, which throws off your probability (which works with "exactly one 6") and hence your asymptotics.