STATEMENT -1: The number of ways in which six different objects can be divided equally into 2 sets is 10.
STATEMENT -2 , The number of ways in which six different objects be distributed equally among two persons is 20.

Options

A. Statement-1 is true ,statement -2 is true , statement -2 is a correct explanation for statement -1
B. Statement -1 is true , statement -2 is true , statement -2 is NOT a correct explanation for statement -1
C. Statement -1 is true , statement -2 is false
D. Statement -1 is false , statement -2 is true

Answer

To solve the problem, we need to verify the two statements regarding the number of ways to divide and distribute six different objects. We will analyze each statement step by step.

### Step 1: Analyze Statement 1
**Statement 1**: The number of ways in which six different objects can be divided equally into 2 sets is 10.

To find the number of ways to divide 6 different objects into 2 equal sets, we can use the formula:
\[ \text{Number of ways} = \frac{n!}{k! \cdot k! \cdot m!} \]
where:
- \( n \) is the total number of objects (6 in this case),
- \( k \) is the number of objects in each set (3 objects in each set since we are dividing into 2 sets),
- \( m \) is the number of sets (2 in this case).

Using the formula:
\[ \text{Number of ways} = \frac{6!}{3! \cdot 3! \cdot 2!} \]

Calculating the factorials:
- \( 6! = 720 \)
- \( 3! = 6 \)
- \( 2! = 2 \)

Now substituting these values into the formula:
\[ \text{Number of ways} = \frac{720}{6 \cdot 6 \cdot 2} = \frac{720}{72} = 10 \]

Thus, **Statement 1 is true**.

### Step 2: Analyze Statement 2
**Statement 2**: The number of ways in which six different objects can be distributed equally among two persons is 20.

For distributing 6 different objects equally among 2 persons, we can use a different formula:
\[ \text{Number of ways} = \frac{n!}{k! \cdot (n-k)!} \]
where:
- \( n \) is the total number of objects (6),
- \( k \) is the number of objects each person receives (3).

Using the formula:
\[ \text{Number of ways} = \frac{6!}{3! \cdot 3!} \]

Calculating:
\[ \text{Number of ways} = \frac{720}{6 \cdot 6} = \frac{720}{36} = 20 \]

Thus, **Statement 2 is also true**.

### Conclusion
Both statements are true:
- Statement 1 is true: The number of ways to divide 6 different objects into 2 sets is indeed 10.
- Statement 2 is true: The number of ways to distribute 6 different objects equally among 2 persons is indeed 20.

However, it is important to note that Statement 1 is not a correct explanation for Statement 2 because the context of division and distribution is different.