Question

For which of the values of $n,$ $(n-4)!$ is defined?

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

Answer: (B), (C), (D)

$6$

$\underset{–}{\text{Need to Find}:}$
The values of $n$ for which $(n-4)!$ is defined

As we know, factorial is defined for whole numbers only.

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

So, for $(n-4)!$ to be defined, $(n-4)$ must belong to the set of whole numbers.


As per the above table, for $n$ equals to $4,5$ and $6,$ $(n-4)$ belongs to the set of whole numbers, hence, for these value of $n,$ $(n-4)!$ is defined.