Question

In how many distinct ways can the letters of the word READERS be arranged?​

Answer 1

Answer:

The letters of the word readers can be arranged in 1260 distinct ways.

Step-by-step explanation:

A word has n letters.

The are m repeating letters, each of them repeating $r_{0}, r_{1}, ..., r_{m}$ times

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

$N_{A} = \frac{n!}{r_{1}! \times r_{2}! \times ... \times r_{m}}$

In this question:

Readers.

Has 7 letters.

E repeats twice.

R repeats twice.

So

$N = \frac{7!}{2! \times 2!} = 1260$

The letters of the word readers can be arranged in 1260 distinct ways.