Statement -1 : Let x denotes the number of sixes in 3 consecutive throws of die, then `P(x=3)=1/216`
Statement-2 : The probability that sum of faces appeared is 10, when three dice are rolled is `(""^9C_7)/(6^3)`

Options

A. Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for statement -12
B. Statement-1 is true, Statement-2 is true, Statement-2 is Not a correct explanation for statement -12
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 two statements regarding probabilities related to rolling dice.

### Statement 1:
Let \( X \) denote the number of sixes in 3 consecutive throws of a die. We need to find \( P(X = 3) \).

**Step 1: Calculate the total outcomes when rolling a die three times.**
- When a die is thrown, there are 6 possible outcomes (1, 2, 3, 4, 5, 6).
- Therefore, when rolling a die three times, the total number of outcomes is:
\[ 6^3 = 216 \]

**Step 2: Determine the favorable outcomes for getting three sixes.**
- The only favorable outcome for getting three sixes is (6, 6, 6).
- Thus, the number of favorable outcomes is 1.

**Step 3: Calculate the probability of getting three sixes.**
- The probability \( P(X = 3) \) is given by the ratio of favorable outcomes to total outcomes:
\[ P(X = 3) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{1}{216} \]

**Conclusion for Statement 1:**
- The statement \( P(X = 3) = \frac{1}{216} \) is **true**.

### Statement 2:
We need to find the probability that the sum of the faces when three dice are rolled is 10.

**Step 1: Calculate the total outcomes when rolling three dice.**
- Similar to Statement 1, the total number of outcomes when rolling three dice is:
\[ 6^3 = 216 \]

**Step 2: Find the favorable outcomes for the sum being 10.**
- We need to find combinations of three numbers (from 1 to 6) that add up to 10. The valid combinations are:
1. (4, 3, 3)
2. (5, 4, 1)
3. (5, 3, 2)
4. (6, 3, 1)
5. (6, 2, 2)

**Step 3: Count the arrangements for each combination.**
- (4, 3, 3): Arrangements = \( \frac{3!}{2!} = 3 \)
- (5, 4, 1): Arrangements = \( 3! = 6 \)
- (5, 3, 2): Arrangements = \( 3! = 6 \)
- (6, 3, 1): Arrangements = \( 3! = 6 \)
- (6, 2, 2): Arrangements = \( \frac{3!}{2!} = 3 \)

**Step 4: Calculate the total number of favorable outcomes.**
- Total favorable outcomes = \( 3 + 6 + 6 + 6 + 3 = 24 \)

**Step 5: Calculate the probability of the sum being 10.**
- The probability is given by:
\[ P(\text{sum} = 10) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{24}{216} = \frac{1}{9} \]

**Conclusion for Statement 2:**
- The statement given in the question is \( \frac{9C7}{6^3} \).
- \( 9C7 = \frac{9!}{7! \cdot 2!} = \frac{9 \cdot 8}{2} = 36 \).
- Thus, \( \frac{9C7}{6^3} = \frac{36}{216} = \frac{1}{6} \), which is not equal to \( \frac{1}{9} \).
- Therefore, Statement 2 is **false**.

### Final Conclusion:
- Statement 1 is **true**.
- Statement 2 is **false**.