Let S be the set of integer solutions to the equation ri + r2 +13+x4 = 30, where ri >0 for i = 1,2, 3, 4. That is, S= {(r1, 12, 13, 14) | r; € Z and ri > 0 and ri + 12 + 13 + 14 = 30}. (a) Find |S]. For i = 1,2,3, 4, define A, = {(r1, r2, 13, 14) ES|r; > 10}. (b) Find JA| for each i. (c) For each 1

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