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

Options

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

Explanation

To solve the expression \(\frac{8!}{6! \times 2!}\), we will follow these steps:

### Step 1: Write the factorials in expanded form
We know that:
- \(8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\)
- \(6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1\)
- \(2! = 2 \times 1\)

### Step 2: Substitute the factorials into the expression
Now, we can substitute these values into our expression:
\[ \frac{8!}{6! \times 2!} = \frac{8 \times 7 \times 6!}{6! \times (2 \times 1)} \]

### Step 3: Cancel out the common terms
Notice that \(6!\) appears in both the numerator and the denominator, so we can cancel it out:
\[ = \frac{8 \times 7}{2 \times 1} \]

### Step 4: Simplify the expression
Now, we can simplify the expression:
\[ = \frac{8 \times 7}{2} = \frac{56}{2} = 28 \]

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

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