Question 6
of 14 Step 1 of 1

Evaluate the following expression.
\[
\frac{7 !}{5 !}
\]
Answer How to enter your answer (opens in new window)
5 Points

Step 1 ：The expression is asking for the factorial of 7 divided by the factorial of 5. The factorial of a number is the product of all positive integers less than or equal to that number. For example, the factorial of 5 (denoted as 5!) is \(5 \times 4 \times 3 \times 2 \times 1 = 120\).

Step 2 ：So, to solve this problem, we need to calculate the factorial of 7 and the factorial of 5, and then divide the factorial of 7 by the factorial of 5.

Step 3 ：The factorial of 7 is \(7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040\).

Step 4 ：The factorial of 5 is \(5 \times 4 \times 3 \times 2 \times 1 = 120\).

Step 5 ：Dividing the factorial of 7 by the factorial of 5 gives us \(\frac{5040}{120} = 42\).

Step 6 ：Final Answer: The result of the expression \(\frac{7 !}{5 !}\) is \(\boxed{42}\).