In each question consist of five statements (a-e) followed by options consisting of three statements put together in a specific order. Choose the option which indicates a valid argument, that is, where the third statement is a conclusion drawn from the preceding two statements.

a. all captains are great players.
b. some captains are successful sports administrators.
c. Ritwik is a great player.
d. Ritwik is a captain and successful sports administrator.
e. some successful sports administrators are great players.

Choose the correct option:

The correct option is a b e.

Let us analyze the three statements given in the order (a, b, e) to determine if statement (e) logically follows as a valid conclusion from premises (a) and (b):

Statement a (Premise 1): All captains are great players.
Statement b (Premise 2): Some captains are successful sports administrators.
Statement e (Conclusion): Some successful sports administrators are great players.

Logical Reasoning:
From premise (b), we know there is an intersection between the group of "captains" and the group of "successful sports administrators". That is, there exist individuals who are both captains and successful sports administrators.
From premise (a), every individual who is a captain is also a "great player".
Therefore, those individuals who are both captains and successful sports administrators must also be great players. This logically implies that some successful sports administrators are indeed great players.

Thus, the sequence a b e forms a valid logical syllogism where statement (e) is a valid conclusion drawn from statements (a) and (b).