Question

How many arrangements can be made out of the letters of the word
'ENGINEERING' [order is not important] + [without repetition of letters]

Answer 1

The number of ways the arrangements can be made out of the letters of the word

'ENGINEERING' [order is not important] + [without repetition of letters] is as follows.

Given:

The word ENGINEERING.

To find:

The number of ways the arrangements can be made out of the letters of the word 'ENGINEERING'

Solution:

There are a total of 11 letters.

In this word there are, 3 E's, 3 N's, 2 G's, 2 I's and 1 R.

In order to find the number of ways a word can be arranged without repetition of letters is given by,

= 11! / ( 3! × 3! × 2! × 2! )

= 39916800 / ( 6 × 6 × 2 × 2 )

= 6652800  / ( 6 × 2 × 2 )

= 1108800  / ( 2 × 2 )

= 554400 / 2

= 277200

Therefore, in 277200 ways the word ENGINEERING can be arranged without repetition of letters.