Statement-1: The coefficient of `a^(3)b^(4)c^(3)` in the expansion of `(a-b+c)^(10)` is `(10!)/(3!4!3!)`
Statement-2: The coefficient of `x^(p)y^(p)z^(r)` in the expansion of `(x+y+z)^(n)` is `(n!)/(p!q!r!)` for all integer n.

Answer

To solve the problem, we need to analyze the two statements provided and verify their correctness based on the multinomial theorem.

### Step 1: Understanding the Multinomial Theorem
The multinomial theorem states that for any positive integer \( n \) and any non-negative integers \( p, q, r \) such that \( p + q + r = n \), the expansion of \( (x_1 + x_2 + x_3)^n \) can be expressed as:

\[ (x_1 + x_2 + x_3)^n = \sum_{p+q+r=n} \frac{n!}{p!q!r!} x_1^p x_2^q x_3^r \]

### Step 2: Analyzing Statement 1
We need to find the coefficient of \( a^3 b^4 c^3 \) in the expansion of \( (a - b + c)^{10} \).

- Here, \( n = 10 \), \( p = 3 \) (for \( a \)), \( q = 4 \) (for \( -b \)), and \( r = 3 \) (for \( c \)).
- According to the multinomial theorem, the coefficient of \( a^3 (-b)^4 c^3 \) is given by:

\[ \frac{10!}{3!4!3!} \]

- The negative sign from \( (-b)^4 \) will not affect the coefficient itself, as we are only interested in the numerical coefficient.

### Step 3: Conclusion for Statement 1
Thus, the coefficient of \( a^3 b^4 c^3 \) in \( (a - b + c)^{10} \) is indeed \( \frac{10!}{3!4!3!} \). Therefore, Statement 1 is **True**.

### Step 4: Analyzing Statement 2
Statement 2 claims that the coefficient of \( x^p y^q z^r \) in the expansion of \( (x + y + z)^n \) is given by:

\[ \frac{n!}{p!q!r!} \]

- This is a direct application of the multinomial theorem, where \( p + q + r = n \).
- Since this holds true for all integers \( n \) and non-negative integers \( p, q, r \), Statement 2 is also **True**.

### Final Conclusion
Both statements are true. Statement 2 provides a valid reason for the correctness of Statement 1.