Three randomly chosen non negative integers $x, y, z$ are found to satisfy the equation $x + y + z = 10$ . Then the probability that $z$ is even, is

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Three randomly chosen non negative integers x , y , z are found to satisfy the equation x + y + z = 10 . Then the probability that z is even, is

TestHub · Accepted Answer

Let z = 2 k , where k = 0 , 1 , 2 , 3 , 4 , 5 ∴ x + y = 10 - 2 k Number of non negative integral solutions ∑ k = 0 5 11 - 2 k C 1 = ∑ 11 - 2 k = 3 6 Total cases = 10 + 3 - 1 C 3 - 1 = 66 Required probability = 36 66 = 6 11

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