Nikita has three coins. One coin is fair, one coin is biased so that the probability of obtaining a head is $$\(\frac{1}{3}\)$$ and the third coin is biased so that the probability of obtaining a head is $$\(\frac{1}{5}\)$$. The random variable $$\(X\)$$ is the number of heads that Nikita obtains when he throws all three coins at the same time. Find the probability generating function of $$\(Z\)$$, expressing your answer as a polynomial. ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ .

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