Question

Write the product $5\times 6\times 7\times 8\times 9$ in factorial notation.

• A. $\frac{9!}{4}$
• B. $\frac{9}{4!}$
• C. $\frac{9!}{4!}$
• D. $\frac{9}{4}$

Answer 1

The correct option is C $\frac{9!}{4!}$

$\underset{–}{\text{Need to Write}:}$
The product $5\times 6\times 7\times 8\times 9$ in factorial notation.

$5\times 6\times 7\times 8\times 9$,
In the given product if we multiply $1\times 2\times 3\times 4$, it will give $9!$ .
$9!=1\times 2\times 3\times 4\times 5\times 6\times 7\times 8\times 9$

Thus, by multiplying and dividing $1\times 2\times 3\times 4$ in the product, we will get,

$=\frac{1\times 2\times 3\times 4\times 5\times 6\times 7\times 8\times 9}{1\times 2\times 3\times 4}$

$=\frac{9!}{4!}$ $(\because 1\times 2\times 3\times ...n=n!)$

Therefore option (c.) is the correct choice.