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  • How many different 4-letter words can be made using the letters A through G, with at least one letter repeated?Option: 1 <img alt="4^7-{ }^

How many different 4-letter words can be made using the letters A through G, with at least one letter repeated?

Option: 1

4^7-{ }^4 P_7


Option: 2

4^7+{ }^4 P_7


Option: 3

7^4-{ }^7 P_4


Option: 4

7^4+{ }^7 P_4


Answers (1)

best_answer

From A to G, there are 7 letters.

The total number of 4-letter words that can be formed using 7 different letters (with or without repetition). Because each position in the 4-letter word can be filled in 4 different ways.

So, the required number is 7^4

The number of 4-letter words that can be formed with 7 different digits, with no digit repeated. 

So, the number is  ^7 P_{4}

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 4-letter words can be formed in 7^4-{}^7 P_{4} ways

 

Posted by

Rishabh

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