The principal of a school invited the 280 third-year students to participate in a game. Suppose there are 5 objects and 6 characters in a house with 9 rooms; one of the characters hides one of the objects in one of the rooms of the house. The objective of the game is to guess which object was hidden by which character and in which room of the house the object was hidden. All students decided to participate. Each time a student is drawn and gives their answer. The answers must always be different from the previous ones, and the same student cannot be drawn more than once. If the student's answer is correct, they are declared the winner and the game is ended. The principal knows that some student will get the answer right because there are (A) 10 more students than possible distinct answers. (B) 20 more students than possible distinct answers. (C) 119 more students than possible distinct answers. (D) 260 more students than possible distinct answers. (E) 270 more students than possible distinct answers.
The principal of a school invited the 280 third-year students to participate in a game. Suppose there are 5 objects and 6 characters in a house with 9 rooms; one of the characters hides one of the objects in one of the rooms of the house. The objective of the game is to guess which object was hidden by which character and in which room of the house the object was hidden.
All students decided to participate. Each time a student is drawn and gives their answer. The answers must always be different from the previous ones, and the same student cannot be drawn more than once. If the student's answer is correct, they are declared the winner and the game is ended.
The principal knows that some student will get the answer right because there are\\
(A) 10 more students than possible distinct answers.\\
(B) 20 more students than possible distinct answers.\\
(C) 119 more students than possible distinct answers.\\
(D) 260 more students than possible distinct answers.\\
(E) 270 more students than possible distinct answers.