Question

Which of the following has(have) the same value as $7!?$

• A. $6!$
• B. $7\times 6!$
• C. $6\times 5!$
• D. $7\times 6\times 5!$

Answer 1

Answer: (B), (D)

$7\times 6\times 5!$

The factorial of any number is, the given number, multiplied by the factorial of the previous number. So, $8!=8\times 7!$ And $9!=9\times 8!$ .
Like this if we have $n$ factorial then it can be written as, $n!=n\times (n-1)!$

Therefore, $7$ factorial can be written as,
$7!=7\times 6!$
$=7\times 6\times 5!$ $(\because 6!=6\times 5!)$

Hence, $7!$ is equal to $\underset{–}{7\times 6!}$ and $\underset{–}{7\times 6\times 5!}$ but $6!$ and $6\times 5!$