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  • How many different 6-letter words can be formed using the letters A-F with at least one letter repeated?Option: 1 <img alt="5^{6}

How many different 6-letter words can be formed using the letters A-F with at least one letter repeated?

Option: 1

5^{6}\ +\ ^{5}P_{6}


Option: 2

6^{5}\ +\ ^{6}P_{5}  

 

 


Option: 3

5^{6}\ -\ ^{5}P_{6}   


Option: 4

6^{5}\ -\ ^{6}P_{5}   


Answers (1)

best_answer

From A to F, there are six letters.

The total number of 5-letter words that can be formed using 6 different letters (with or without repetition). Because each position in the 5-letter word can be filled in ten different ways, the required number is  6^{5}.

The number of 5-letter words that can be formed with 6 different digits, with no digit repeated. This is the number ^{6}P_{5}.

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 6-letter words can be formed by  6^{5}\ -\ ^{6}P_{5}    ways.

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