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

JEE Advanced 2017 Mathematics question

Three randomly chosen nonnegative integers , and are found to satisfy the equation . Then the probability that is even, is

Answer: (B)

Total non-negative solutions: . For even , has

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Question ID VK-026688