How many words can be formed using all the letters of the word 'ENGINEER'?

Question

Accepted Answer

To find the number of arrangements (permutations) of a word with repeating letters, we use the formula for permutations with indistinguishable items.

### Formula:
$$	ext{Number of arrangements} = \frac{n!}{n_1! \cdot n_2! \cdot \dots \cdot n_k!}$$

### Analysis of the word 'ENGINEER':
* Total letters ($n$) = 8
* Frequency of letters:
  * E appears 3 times
  * N appears 2 times
  * G appears 1 time
  * I appears 1 time
  * R appears 1 time

### Calculation:
$$	ext{Total words} = \frac{8!}{3! \cdot 2!} $$
$$	ext{Total words} = \frac{40,320}{6 	imes 2} = \frac{40,320}{12} = 3,360$$

**Answer:** **3,360** words can be formed.

How many words can be formed using all the letters of the word 'ENGINEER'? - DDCET Q&A

How many words can be formed using all the letters of the word 'ENGINEER'?

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