Consider the equation x1 + x2 + x3 + x4 + x5 = 99. Suppose we require that x1, x2, x3, x4, x5 are all non-negative integers, that is to say, xi {0,...

Consider the equation x1 + x2 + x3 + x4 + x5 = 99. Suppose we require that x1, x2, x3, x4, x5 are all non-negative integers, that is to say, xi ∈ {0, 1, 2, . . . , 99} for i = 1, . . . , 5. Suppose that we allow solutions where the different variables can take the same values. For example, one solution is x1 = 0, x2 = 0, x3 = 0, x4 = 0, x5 = 99. Another solution is x1 = 0, x2 = 99, x3 = 0, x4 = 0, x5 = 0. Yet another solution is x1 = 2, x2 = 3, x3 = 3, x4 = 2, x5 = 89. How many different such solutions are there? To receive credit, you must express your answer as a single binomial coefficient, and also justify your answer in a few sentences.