The value of `(453!)/(450!3!)` is

Options

A. greater than `10^(100)`
B. between `10^(10) and 10^(100)`
C. betweenn 10 and `10^(10)`
D. less than 10

Explanation

To solve the expression \(\frac{453!}{450! \cdot 3!}\), we can simplify it step by step.

### Step 1: Simplify the Factorials
We start by rewriting \(453!\) in terms of \(450!\):
\[ 453! = 453 \times 452 \times 451 \times 450! \]
Now, we can substitute this into our original expression:
\[ \frac{453!}{450! \cdot 3!} = \frac{453 \times 452 \times 451 \times 450!}{450! \cdot 3!} \]

### Step 2: Cancel Out \(450!\)
Next, we can cancel \(450!\) from the numerator and the denominator:
\[ = \frac{453 \times 452 \times 451}{3!} \]

### Step 3: Calculate \(3!\)
Now, we need to calculate \(3!\):
\[ 3! = 3 \times 2 \times 1 = 6 \]

### Step 4: Substitute \(3!\) Back into the Expression
Now we can substitute \(3!\) back into our expression:
\[ = \frac{453 \times 452 \times 451}{6} \]

### Step 5: Calculate the Numerator
Now, we calculate the product of \(453\), \(452\), and \(451\):
\[ 453 \times 452 = 204306 \]
\[ 204306 \times 451 = 92151606 \]

### Step 6: Divide by \(6\)
Now, we divide \(92151606\) by \(6\):
\[ \frac{92151606}{6} = 15358601 \]

### Final Result
Thus, the value of \(\frac{453!}{450! \cdot 3!}\) is:
\[ 15358601 \]