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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