Statements: All the actors are girls. All the girls are beautiful.…

Concept: When two universal affirmative ("All") statements share a common middle term arranged in a chain -- All M are P, and All S are M -- transitivity gives a direct universal conclusion, All S are P (the Barbara/AAA-1 form). Separately, a universal affirmative statement, All A are B, also permits a valid conversion to a particular statement, Some B are A, under the standard existential-import convention used in these syllogism questions. Both routes can apply to the same pair of statements at once.

1. Statement 1 places Actors entirely inside Girls, and Statement 2 places Girls entirely inside Beautiful. Chaining the two (Actors -> Girls -> Beautiful) gives Actors -> Beautiful directly, so Conclusion (1), All the actors are beautiful, follows.

2. Statement 1, All the actors are girls, is a universal affirmative statement, so it converts to the particular statement Some girls are actors. This conversion is independent of the chain used above, so Conclusion (2) also follows.

Cross-check: Draw three concentric circles -- Actors innermost, Girls in the middle, Beautiful outermost. Every point inside the Actors circle also lies inside the Girls circle and the Beautiful circle, which is exactly what both derivations above claim.

Since both the direct chain and the conversion hold independently, both conclusions are valid, so the answer is: Both (1) and (2) follows.