Question

Evaluate each expression.



6! =



3! • 2! =



StartFraction 6 factorial Over 3 factorial EndFraction =

Answer 1

To evaluate the expressions given, we will first calculate the factorial values.

1. **Calculate \( 6! \)**:
\[
6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720
\]

2. **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:
\[
3! \cdot 2! = 6 \cdot 2 = 12
\]

3. **Calculate \(\frac{6!}{3!}\)**:
Using the value of \(6!\) calculated earlier:
\[
\frac{6!}{3!} = \frac{720}{6} = 120
\]

In summary, the calculated values are:
- \(6! = 720\)
- \(3! \cdot 2! = 12\)
- \(\frac{6!}{3!} = 120\)