Question: 64. For k 1, n k, how many distinct positive integer vectors (x1, x2, . . . , xk) satisfy the inequality x1

64. For k ≥ 1, n ≥ k, how many distinct positive integer vectors (x1, x2, . . . , xk) satisfy the inequality x1 + x2 + · · · + xk ≥ n?

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