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Three non-negative integers x, y and z are chosen at random such that x + y + z = 10. What is the probability that z is an even number?
- 6/11
- 36/55
- 5/11
- 1/2
Correct answer: 6/11
Solution
Using stars and bars, total solutions = C(12,2) = 66. For z even (z=0,2,4,6,8,10), the number of solutions to x+y=10-z is (11-z+1) summed over even z, giving 36 favorable cases.
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