Question

# (a) How many words with or without meaning, can be formed by using all the letters...

(a) How many words with or without meaning, can be formed by using all the letters of the word, ’DELHI’ using each letter exactly once?

(b) How many words with or without meaning, can be formed by using all the letters of the word, ’ENGINEERING’ using each letter exactly once?

Given That:-

(a) How many words with or without meaning, can be formed by using all the letters of the word, ’DELHI’ using each letter exactly once?

Given,

The word 'DELHI' has 5 letters and all these letters are different.

Total number of words (with or without meaning) That can be formed using all these 5 letters using each letter exactly once

= Number of arrangements of 5 letters taken all at a time

= 5!

= 5 x 4 x 3 x 2 x 1

=120

(b) How many words with or without meaning, can be formed by using all the letters of the word, ’ENGINEERING’ using each letter exactly once?

The word 'ENGINEERING' contains 11 letters, with 3E, 3N, 2G, 2I and IR.

The number of arrangements = 11!/(3!3!2!2!1!)

= 277200