Question

For which of the following value(s) of $n$, $(\frac{6}{n})!$ will be defined?

• A. $1$
• B. $2$
• C. $3$
• D. $4$
• E. $6$

Answer 1

Answer: (A), (B), (C), (E)

$6$

$\underset{–}{\text{Need to Identify}:}$
The values of $n,$ for which $(\frac{6}{n})!$ is defined

As we know, for $(\frac{6}{n})!$ to be defined, $(\frac{6}{n})$ must be a whole number.

$\underset{–}{\text{Whole numbers}:}$
Whole numbers are collection of positive integers and zero. It is represented by the symbol “W” and the set of numbers are $\{0,1,2,3,4,5,6,7,8,9,\dots \}$


$(\frac{6}{n})$ can be rewitten as

$(\frac{3\times 2\times 1}{n})$

As we can see that $1,2$ and $3$ are the factors of $6,$ $(\frac{6}{n})$ will be a whole number for $n$ equals to $1,2,3$ and $6$. Hence, for these values of $n,$ $(\frac{6}{n})!$ will be defined.