Compute `(8!)/(6!xx2!)`

Options

A. 7
B. 14
C. 31
D. 28

Explanation

To compute \(\frac{8!}{6! \times 2!}\), we can follow these steps:

### Step 1: Write the factorials in expanded form
We start by expressing \(8!\) in terms of \(6!\):
\[ 8! = 8 \times 7 \times 6! \]
So we can rewrite the expression:
\[ \frac{8!}{6! \times 2!} = \frac{8 \times 7 \times 6!}{6! \times 2!} \]

### Step 2: Cancel out \(6!\)
Since \(6!\) appears in both the numerator and the denominator, we can cancel it out:
\[ \frac{8 \times 7 \times \cancel{6!}}{\cancel{6!} \times 2!} = \frac{8 \times 7}{2!} \]

### Step 3: Simplify \(2!\)
Now we need to calculate \(2!\):
\[ 2! = 2 \times 1 = 2 \]
Substituting this into our expression gives:
\[ \frac{8 \times 7}{2} \]

### Step 4: Perform the division
Now we can simplify \(\frac{8 \times 7}{2}\):
\[ \frac{8 \times 7}{2} = \frac{56}{2} = 28 \]

### Final Answer
Thus, the value of \(\frac{8!}{6! \times 2!}\) is:
\[ \boxed{28} \]

---