Consider the set S={1,2,3,...,1441}. 1. Nora counts thoses subsets of S having exactly two elements, tbe sum of which is even. Rania counts those subsets of S having exactly two elements, the sum of which is odd. Determine the numbers counted by Nora and Rania. 2. Let t be the number of subsets of S which have at least two elements and the product of the elements is even. Determine the greatest power of 2 which divides t. 3. Ahmad counts the subsets of S having 77 elements such that in each subset the sum of the elements is even. Bushra counts the subsets of S having 77 elements such that in each subset the sum of the elements is odd. Whose number is bigger? Determine the difference between the numbers found by Ahmad and Bushra.