alexchan41
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How many distinct permutations can be made from the letters of the word

“INDEPENDENCE”?


if anyone could answer, thank you (^-^)​

Respuesta :

AlexSchreiber

Answer:

360

Step-by-step explanation:

Word INDEPENDENCE has I−1, N−3, D−2, E−4, P−1, C−1

There are six different letters in INDEPENDENCE

Now according to the question, we need to form 4 different letter words, So the selection of 4 words out of 6 is  

[tex]^{6}C _{4}[/tex]

​

 and making its arrangements

So total number of ways is  

[tex]^{6}C _{4}[/tex] ×4!=360

The number of distinct permutations can be made from the letters of the word “INDEPENDENCE” is; 1663200

We are given the word INDEPENDENCE and it has;

  • I − one
  • N - three
  • D − two
  • E - four
  • P - one
  • C - one

Thus, we see that there are six different letters and 12 letters in total in INDEPENDENCE

Now from the question, the distinct permutations that can be formed is;

12!/(3! × 2! × 4!) = 1663200

Read more on permutations at; https://brainly.com/question/12468032

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