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Evaluate each expression.

[tex]\[ 6! = \square \][/tex]

[tex]\[ 3! \cdot 2! = \square \][/tex]

[tex]\[ \frac{6!}{3!} = \square \][/tex]

Sagot :

GinnyAnsweridn
Let's evaluate each of the given expressions step-by-step.

### 1. Evaluating [tex]\( 6! \)[/tex]

The factorial of a number [tex]\( n \)[/tex] is the product of all positive integers from 1 to [tex]\( n \)[/tex]. So, for [tex]\( 6! \)[/tex], we have:

[tex]\[ 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \][/tex]

Therefore,

[tex]\[ 6! = 720 \][/tex]

### 2. Evaluating [tex]\( 3! \cdot 2! \)[/tex]

First, we find [tex]\( 3! \)[/tex] and [tex]\( 2! \)[/tex]:

[tex]\[ 3! = 3 \times 2 \times 1 = 6 \][/tex]
[tex]\[ 2! = 2 \times 1 = 2 \][/tex]

Now, multiply these two results together:

[tex]\[ 3! \cdot 2! = 6 \cdot 2 = 12 \][/tex]

Therefore,

[tex]\[ 3! \cdot 2! = 12 \][/tex]

### 3. Evaluating [tex]\( \frac{6!}{3!} \)[/tex]

We already know [tex]\( 6! \)[/tex] and [tex]\( 3! \)[/tex]:

[tex]\[ 6! = 720 \][/tex]
[tex]\[ 3! = 6 \][/tex]

Now, divide [tex]\( 6! \)[/tex] by [tex]\( 3! \)[/tex]:

[tex]\[ \frac{6!}{3!} = \frac{720}{6} = 120 \][/tex]

Therefore,

[tex]\[ \frac{6!}{3!} = 120 \][/tex]

### Final Results

So, the evaluated expressions are as follows:

[tex]\[ 6! = 720 \][/tex]
[tex]\[ 3! \cdot 2! = 12 \][/tex]
[tex]\[ \frac{6!}{3!} = 120 \][/tex]
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