Question

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

Answer 1

There are 60 permutations.

Explanation:

Arrangements formula:

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

`A_n = n!`

With repetition:

For each element that repeats, with
`n_1, n_2, ..., n_n` times, the formula is:

`A_n^(n_1,n_2,...,n_n) = (n!)/(n_1!n_2!...n_n)`

In this question:

Apple has 5 letters.

P appears two times. So

`A _5^(2) = (5!)/(2!) = 60`

There are 60 permutations.