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If a small monster collector has 20 small monster containment devices; intends to use all of...

If a small monster collector has 20 small monster containment devices; intends to use all of those devices; has access to non-unique Water, Fire and Grass type small monsters; intends to capture at least two small monsters of each type; and intends to capture at least three Fire-type small monsters - how many different combinations of small monster types can that collector capture?

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