Question

1. How many different letter arrangements can be made from the following words (the arrangements don’t need to be meaningful)? Letters are not unique (e.g. F₁ is the same thing as F₂)
   
   a) WORDS
   b) DIFFERENT

Answer 1

Solution:

We have to find number of different  letter arrangements can be made from the following words.

Part a) WORDS

Since all letters are different ,we use formula nPr

n = total objects = total letters = 5

r = number of objects selected for arrangements = 5

Thus find: 5P5 by using permutation formula:

( Note : 0! = 1)

Thus there is 120 different arrangements of letters of word : WORDS.

Part b) DIFFERENT

n = total letters = 9

n₁ = Number of times D occurs = 1

n₂ = Number of times I occurs = 1

n₃ = Number of times F occurs = 2

n₄ = Number of times E occurs = 2

n₅ = Number of times R occurs = 1

n₆ = Number of times N occurs = 1

n₇ = Number of times T occurs = 1

Thus the number of different permutations

Thus number of different arrangements of letters of the word DIFFERENT are = 90720