To evaluate the expressions given, we will first calculate the factorial values.
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Calculate \( 6! \): \[ 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \]
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Calculate \( 3! \cdot 2! \):
- First, calculate \( 3! \): \[ 3! = 3 \times 2 \times 1 = 6 \]
- Then calculate \( 2! \): \[ 2! = 2 \times 1 = 2 \]
- Now, multiply the two results: \[ 3! \cdot 2! = 6 \cdot 2 = 12 \]
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Calculate \(\frac{6!}{3!}\): Using the value of \(6!\) calculated earlier: \[ \frac{6!}{3!} = \frac{720}{6} = 120 \]
In summary, the calculated values are:
- \(6! = 720\)
- \(3! \cdot 2! = 12\)
- \(\frac{6!}{3!} = 120\)