Four numbers are chosen at random from the numbers \( 1,2,3, \ldots...

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Four numbers are chosen at random from the numbers \( 1,2,3, \ldots, 20 \). Let \( p_{e}\left(p_{0}\right) \) denote the probability that their sum is even (odd).
(a) \( p_{e}-p_{0}=3 / 323 \)
(b) \( p_{e}=163 / 323 \)
(c) \( p_{0}p_{e} \)
(d) \( p_{e}p_{0} \)
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