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  •  How many different 4-letter words can be formed using the letters from the word "INDEPENDENCE"?  Option: 1 1152</d

 How many different 4-letter words can be formed using the letters from the word "INDEPENDENCE"?

 

Option: 1

1152


Option: 2

576


Option: 3

288


Option: 4

144


Answers (1)

best_answer

The word "INDEPENDENCE" has 13 letters. To form a 4-letter word, we need to choose 4 letters from these 13 letters. Since there are repetitions of certain letters (E, N, and P), we need to consider the number of arrangements with repetitions.

The total number of arrangements is given by 13P4, which is equal to \frac{13 !}{(13-4) !}=15120 However, since the repetitions of the letters E, N, and P will result in the same word, we need to divide the total arrangements by the repetitions. The letter E appears twice, so we divide by 2 ! ,the letter N appears three times, so we divide by 3!, and the letter P appears twice, so we divide by 2 !

Therefore, the correct answer is \frac{15120}{2 ! \times 3 ! \times 2 !}=288

 

Posted by

Irshad Anwar

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