If the result of the summoning is random, find the probability that at least one master is successfully matched to his favorite servant.?

Six individuals (known as masters) are chosen to attend the next Holy Grail War. Each masters is required to summon a servant from three candidate classes: saber, lancer, and caster. Masters are equally grouped into three groups, denoted as ss, ll, and cc, who want to summon two sabers, two lancers and two casters... show more Six individuals (known as masters) are chosen to attend the next Holy Grail War. Each masters is required to summon a servant from three candidate classes: saber, lancer, and caster. Masters are equally grouped into three groups, denoted as ss, ll, and cc, who want to summon two sabers, two lancers and two casters respectively. Masters in the same team are in favor of servants from the same class. If the result of the summoning is random, find the probability that at least one master is successfully matched to his favorite servant.
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