Conquer the College Math Placement Challenge 2026 – Step Up and Shine!

To find the value of \( \frac{9!}{7!} \), it helps to understand how factorials work. The factorial of a number \( n \), denoted as \( n! \), is the product of all positive integers from \( 1 \) to \( n \).

First, it is useful to expand the factorials involved:

- \( 9! = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \)

- \( 7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \)

When we divide \( 9! \) by \( 7! \), many terms cancel out:

\[

\frac{9!}{7!} = \frac{9 \times 8 \times 7!}{7!}

\]

The \( 7! \) in the numerator and denominator cancel, leaving us with:

\[

9 \times 8

\]

Now, we perform the multiplication:

\[

9 \times 8 = 72

\]

Therefore