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Three randomly chosen non–negative integers x, y and z are found to satisfy the equation x + y + z = 10.

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

(a) 36/55

(b) 6/11

(c) 1/2

(d) 5/11.

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(B) Total number of non negative solutions of x + y + z = 10 are = 12C2 = 66 (using n+r–1Cr–1)
If z is even then there can be following cases:

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