There are total 120 ways to arrange the letters of word "COUNT".
What is permutation?
A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.
Permutation Formula
[tex]nP_{r} =\frac{n!}{(n-r)!}[/tex]
Where,
P is the number of arrangements.
r is the of objects selected.
n is the total numbers of object.
According to the question.
We have a word "COUNT".
Total number of letters in word "COUNT" is 5.
⇒ Total number of objects, n = 5
Since, we have to form different words by using 5 letters of count.
⇒ Total number of objects we have to select, r = 5
Therefore, the total number of ways to arrange the letters of "COUNT" is given by
[tex]5P_{5}=\frac{5!}{(5-5)!}[/tex]
⇒[tex]5P_{5} =\frac{5!}{0!}[/tex]
⇒[tex]5P_{5} =\frac{5!}{1}[/tex] (because,0! = 1)
⇒[tex]5P_{5} = 5(4)(3)(2) = 120 ways[/tex]
Hence, there are total 120 ways to arrange the letters of word "COUNT".
Find out more information about permutation here:
https://brainly.com/question/2295036
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