Compute `(12!)/((10)!(2)!)`.

Answer

To solve the expression \(\frac{12!}{10! \cdot 2!}\), we can follow these steps:

### Step 1: Write out the factorials
We know that:
- \(12! = 12 \times 11 \times 10!\)
- \(10! = 10 \times 9 \times 8 \times \ldots \times 1\)
- \(2! = 2 \times 1 = 2\)

### Step 2: Substitute \(12!\) in the expression
Substituting \(12!\) into the expression, we have:
\[ \frac{12!}{10! \cdot 2!} = \frac{12 \times 11 \times 10!}{10! \cdot 2!} \]

### Step 3: Cancel \(10!\)
Now, we can cancel \(10!\) from the numerator and the denominator:
\[ \frac{12 \times 11 \times \cancel{10!}}{\cancel{10!} \cdot 2!} = \frac{12 \times 11}{2!} \]

### Step 4: Substitute \(2!\)
Now, substituting \(2!\) into the expression:
\[ \frac{12 \times 11}{2} = \frac{12 \times 11}{2 \times 1} = \frac{12 \times 11}{2} \]

### Step 5: Perform the multiplication and division
Calculating the multiplication:
\[ 12 \times 11 = 132 \]
Now divide by 2:
\[ \frac{132}{2} = 66 \]

### Final Answer
Thus, the value of \(\frac{12!}{10! \cdot 2!}\) is \(66\).

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