The number of positive intergers satisfying the in-equality `""^(n+1)C_(n-2)-""^(n+1)C_(n-1)le100`, is

Options

A. 6
B. 8
C. 5
D. none of these

Explanation

To solve the inequality \(\binom{n+1}{n-2} - \binom{n+1}{n-1} \leq 100\), we will follow these steps:

### Step 1: Rewrite the Combinations
Using the property of combinations, we know that:
\[ \binom{n+1}{n-2} = \binom{n+1}{3} \quad \text{and} \quad \binom{n+1}{n-1} = \binom{n+1}{2} \]
Thus, we can rewrite the inequality as:
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