Questions: Evaluate the factorial expression. 27!/22! 27!/22!=

Evaluate the factorial expression. 27!/22! 27!/22!=
Transcript text: Evaluate the factorial expression. \[ \begin{array}{l} \frac{27!}{22!} \\ \frac{27!}{22!}= \end{array} \]
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Solution

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Solution Steps

Step 1: Simplifying the Factorial Expression

We start with the expression:

\[ \frac{27!}{22!} \]

To simplify this, we can cancel out the common factorial terms. This gives us:

\[ \frac{27!}{22!} = 27 \times 26 \times 25 \times 24 \times 23 \]

Step 2: Calculating the Product

Now, we calculate the product of the descending integers from 27 to 23:

\[ 27 \times 26 = 702 \] \[ 702 \times 25 = 17550 \] \[ 17550 \times 24 = 421200 \] \[ 421200 \times 23 = 9687600 \]

Final Answer

Thus, the value of the expression is:

\[ \boxed{9687600} \]

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