Find the value of `""^(4)P_(3)`.

Answer

To find the value of \( 4P3 \), we will use the formula for permutations, which is given by:

\[ nPr = \frac{n!}{(n - r)!} \]

Where \( n \) is the total number of items, and \( r \) is the number of items to arrange.

### Step 1: Identify the values of \( n \) and \( r \)
In this case, we have:
- \( n = 4 \)
- \( r = 3 \)

### Step 2: Substitute the values into the formula
Now we can substitute these values into the permutation formula:

\[ 4P3 = \frac{4!}{(4 - 3)!} \]

### Step 3: Simplify the expression
Calculating \( (4 - 3)! \):

\[ (4 - 3)! = 1! = 1 \]

So, we can rewrite the expression as:

\[ 4P3 = \frac{4!}{1!} \]

### Step 4: Calculate \( 4! \)
Now we need to calculate \( 4! \):

\[ 4! = 4 \times 3 \times 2 \times 1 = 24 \]

### Step 5: Substitute back into the equation
Now we can substitute \( 4! \) and \( 1! \) back into our equation:

\[ 4P3 = \frac{24}{1} = 24 \]

### Final Answer
Thus, the value of \( 4P3 \) is:

\[ \boxed{24} \]