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Two numbers and are chosen at random (with out replacement) from the set \( \{1,2,3 \), \( \ldots, 5 n \). the probability that \( n_{1}^{4}-n_{2}^{4} \) is divisible by 5 , is equal to
(A) \( \frac{n-1}{5 n-1} \)
(B) \( \quad \frac{4(4 n-1)}{5(5 n-1)} \)
(C) \( \frac{17 n-5}{5(5 n-1)} \)
(D) \( \quad \frac{8 n}{5(5 n-1)} \)
\( \mathrm{P} \)
W
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