The correct statements of the following

Options

A. `100!+1` is not divisible by any natural number between `2` and `100`.
B. If `n` objects in a row, then the number of ways of selecting two of these objects such that they are not next to each other is `.^(n-1)C_(2)`.
C. The number of ways in which we can arrange 20 white identical and 20 black identical balls in a row, so that neighbouring balls are of different colors is 2
D. none of these

Explanation

To solve the problem, we need to analyze each statement provided and determine whether they are correct or not.

### Step-by-Step Solution:

**Statement 1: "100 factorial plus 1 is not divisible by any natural number between 2 and 100."**

1. **Understanding 100 factorial (100!)**:
- 100! = 100 × 99 × 98 × ... × 2 × 1, which is an even number since it includes the factor 2.
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