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Let n ≥ 5 be an integer. If 9 n – 8n – 1 = 64 α and 6 n – 5n – 1 = 25 β , then α – β is equal to

1. 1 + 3 n 2 n C ) 5 – 8 ( C + (8 2 – 5 2 ) +.....+ n C n (8 n–1 – 5 n–1 )
2. 1 + 4 n 3 n C ) 5 – 8 ( C + (8 2 – 5 2 ) +.....+ n C n (8 n–2 – 5 n–2 )
3. 4 n 3 n C ) 5 – 8 ( C + (8 2 – 5 2 ) +.....+ n C n (8 n–2 – 5 n–2 )
4. 5 n 4 n C ) 5 – 8 ( C + (8 2 – 5 2 ) +.....+ n C n (8 n–3 – 5 n–3 )

Correct answer: 4 n 3 n C ) 5 – 8 ( C + (8 2 – 5 2 ) +.....+ n C n (8 n–2 – 5 n–2 )

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