Question

How many different arrangements can be made using all the letters in the word topic

Answer 1

The formula to find the permutations is nPr = $\frac{n!}{(n-r)!}$

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 = $\frac{5!}{(5-5)!} =\frac{5!}{0!} = 5!=120$

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

Answer 2

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

Answer: There are 120 different arrangements.