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  • With at least one letter repeated, how many different eight-letter words can be created using the letters A through J?  Option: 1</stron

With at least one letter repeated, how many different eight-letter words can be created using the letters A through J?

 

Option: 1

10^{5}-^{10}P_5


Option: 2

10^{8}-^{10}P_8


Option: 3

10^{7}-^{10}P_7


Option: 4

10^{7}-^{10}P_7


Answers (1)

best_answer

From A to J, there are 10 letters.

The total number of 8-letter words that can be formed using 10 different letters (with or without repetition). Because each position in the 8-letter word can be filled in 8 different ways.

So, the required number is 10^{8} 

The number of 8-letter words that can be formed with 10 different digits, with no digit repeated. 

So, the number is 10^{8} 

The difference between these two numbers is the answer. Now, from the set of all the words, remove those that have no letter repetition, and you have the set.

Therefore, the different 8-letter words can be formed in  10^{8}-^{10}P_8  ways

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Sayak

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