Question 8: In this exercise, we consider strings that can be obtained by reordering the letters of the word ENGINE Determine the number of strings that can be obtained Determine the number of strings in which the two letters E are next to each other Determine the number of strings in which the two letters E are not next to each other and the two letters N are not next to each other (You do not get marks if you write out all possible strings. You must use the counting rules that you learned in class.) Question 9: The square in the left figure below is divided into nine cells. In each cell, we write one of the numbers -1, 0, and 1 Use the Pigeonhole Principle to prove that, among the rows, columns, and main diagonal:s there exist two that have the same sum. For example, in the right figure below, both main diagonals have sum 0. (Also, the two topmost rows both have sum 1, whereas the bottom row and the right column both have sum -2.) 10-1