`(6!)/(3!)`______

Answer

To solve the expression \((6!)/(3!)\), we will follow these steps:

### Step 1: Understand Factorials
Factorials are defined as the product of all positive integers up to a certain number. For example:
- \(n! = n \times (n-1) \times (n-2) \times \ldots \times 1\)

### Step 2: Write Out the Factorials
We will write out \(6!\) and \(3!\):
- \(6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1\)
- \(3! = 3 \times 2 \times 1\)

### Step 3: Substitute the Factorials into the Expression
Now we can substitute these into our expression:
\[ \frac{6!}{3!} = \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1} \]

### Step 4: Cancel Out the Common Terms
Notice that \(3!\) (which is \(3 \times 2 \times 1\)) appears in both the numerator and the denominator. We can cancel these terms:
\[ \frac{6 \times 5 \times 4 \times \cancel{3 \times 2 \times 1}}{\cancel{3 \times 2 \times 1}} = 6 \times 5 \times 4 \]

### Step 5: Calculate the Remaining Product
Now, we will calculate \(6 \times 5 \times 4\):
- First, calculate \(6 \times 5 = 30\)
- Then, multiply \(30 \times 4 = 120\)

### Final Answer
Thus, the value of \(\frac{6!}{3!}\) is \(120\).

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