jennifer84104 jennifer84104
  • 23-05-2020
  • Mathematics
contestada

Find the number of unique permutations of the letters in the word: EXTENT
720
180
900
36

Respuesta :

joaobezerra joaobezerra
  • 31-05-2020

Answer:

180

Step-by-step explanation:

A word has n letters.

There are m repeating letters, each of them repeating [tex]r_{0}, r_{1}, ..., r_{m}[/tex] times

So the number of distincts ways the letters can be permutated is:

[tex]N_{A} = \frac{n!}{r_{1}! \times r_{2}! \times ... \times r_{m}}[/tex]

In this question:

Extent has 6 letters.

E and r repeat 2 times. So

[tex]N = \frac{6!}{2!*2!} = 180[/tex]

So the answer is 180.

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