Question

Which of the following has/have the value equal to the value of $3!?$

• A. $\frac{6!}{2!}$
• B. $(\frac{6}{2})!$
• C. (a) and (b) above.

Answer 1

The correct option is B $(\frac{6}{2})!$

The value of $3!=3\times 2\times 1=6$

Now, let's find the value value of expressions in option (a.) and option (b.) one-by-one:

$\bullet$ Option (a.) $\frac{6!}{2!}$

$\frac{6!}{2!}=\frac{6\times 5\times 4\times 3\times 2!}{2!}$

$\Rightarrow \frac{6!}{2!}=6\times 5\times 4\times 3=360,$ which is not equal to $6.$ Hence, the value of $\frac{6!}{2!}$ is not euqal to the value of $3!$.

$\bullet$ Option (b.) $(\frac{6}{2})!$

$(\frac{6}{2})!=(\frac{2\times 3}{2\times 1})!=(\frac{3}{1})!=3!=6,$ hence, the value of $(\frac{6}{2})!$ is equal to the value of $3!$

Therefore, option (b.) is the correct choice.