Respuesta :

Number of difference arrangements = 5! = 5 x 4 x 3 x 2 x 1 = 120

Answer: There are 120 different arrangements.

The formula to find the permutations is nPr = [tex] \frac{n!}{(n-r)!} [/tex]

Here n represents the total number of objects

r represents the number of objects taken at a time

The word TOPIC has 5 letters.

All the five letters are different.

And we need to take all 5 letters.

Hence n = 5 & r = 5

Number of arrangements = 5P5 = [tex] \frac{5!}{(5-5)!} =\frac{5!}{0!} = 5!=120 [/tex]

120 different arrangements can be made using all the letters in the word TOPIC