ashsundaresan wrote:

Hi all,

This is my first post here, so I apologise if this has been asked.

How many unique ways can you re-arrange the word BOOK if you only select 2 letters?

when I try and do this, the total number of permutations is 12 (4P2)...However, I am not sure how to mathematically calculate the number of duplicates (in this case, there are 5 duplicates)? Ie - BO1 and BO2....I have written down the list of permutations and crossed out the duplicates.

BO1

~~BO2~~

BK

O1B

O1O2

O1K

~~O2B~~

~~O2O1~~

~~O2K~~

KB

KO1

~~KO2~~

Any help appreciated!

The wording of the question is a little convoluted. " re-arrange the word BOOK if you only select 2 letters" is unclear. I think they mean "how many 2 letter words can you make from the letters of the word BOOK"

Out of the letters of the word BOOK, you need to make distinct 2 letter words.

The two letters can be same or they can be different.

Two letters same - This can be done in only 1 way i.e. by selecting both Os. The word will be OO.

Two letters different - Out of the 3 distinct letters (B, O, K), select any two and arrange them in 3p2 = 6 ways.

Total number of distinct 2 letter words = 1+6 = 7

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