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Let \( n \geq 5 \) be an integer. If \( 9^{n}-8 n-1=64 \alpha \) and \( 6^{n}-5 n-1 \) \( =25 \beta \), then \( \alpha-\beta \) is equal to
(a) \( 1+{ }^{n} C_{2}(8-5)+{ }^{n} C_{3}\left(8^{2}-5^{2}\right)+\ldots+{ }^{n} C_{n}\left(8^{n-1}-5^{n-1}\right) \)
(b) \( 1+{ }^{n} C_{3}(8-5)+{ }^{n} C_{4}\left(8^{2}-5^{2}\right)+\ldots+{ }^{n} C_{n}\left(8^{n-2}-5^{n-2}\right) \)
(c) \( { }^{n} C_{3}(8-5)+{ }^{n} C_{4}\left(8^{2}-5^{2}\right)+\ldots+{ }^{n} C_{n}\left(8^{n-2}-5^{n-2}\right) \)
(d) \( { }^{n} C_{4}(8-5)+{ }^{n} C_{5}\left(8^{2}-5^{2}\right)+\ldots+{ }^{n} C_{n}\left(8^{n-3}-5^{n-3}\right) \)
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