Quoting the post of Mitch Hunt on this question.
Feel free to add if u any other pointers.
A NUMBER means NUMEROUS.
THE NUMBER, THE NUMBERS, and NUMBERS refer to ACTUAL NUMBERS (such as 5, 127, etc.)
In B, the number (singular) does not agree with include (plural). Eliminate B.
In C, NUMBERS of prizes refers -- strangely -- not to the prizes themselves but to the ACTUAL NUMBERS associated with these prizes. The intended meaning of the sentence is that Seamus Heaney has won A NUMBER of prizes (meaning NUMEROUS prizes). Eliminate C.
In D, the numbers (meaning ACTUAL NUMBERS) cannot include the Nobel Prize and two Book of the Year awards. Eliminate D.
In E, him (an object pronoun) cannot be used to replace Seamus Heaney's (an adjective modifying Irish poetry). Only a NOUN (or a subject pronoun, such as HE) can serve as the antecedent of an object pronoun. Eliminate E.
The correct answer is A.
In A, Seamus Heaney has won A NUMBER of prizes means that the poet has won NUMEROUS prizes.