sarasotipokwal sarasotipokwal
  • 23-07-2021
  • Mathematics
contestada

How many permutations of letter of the word APPLE are there?​

Respuesta :

joaobezerra joaobezerra
  • 28-07-2021

Answer:

There are 60 permutations.

Step-by-step explanation:

Arrangements formula:

The number of possible arrangements of n elements is given by:

[tex]A_n = n![/tex]

With repetition:

For each element that repeats, with [tex]n_1, n_2, ..., n_n[/tex] times, the formula is:

[tex]A_n^{n_1,n_2,...,n_n} = \frac{n!}{n_1!n_2!...n_n}[/tex]

In this question:

Apple has 5 letters.

P appears two times. So

[tex]A _5^{2} = \frac{5!}{2!} = 60[/tex]

There are 60 permutations.

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