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

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Given : The total number of letters in ‘DELHI’ = 5 

To find : Number of words, with or without meanings using all the letters of the word like eldhi or dehil etc. 

Formula used : 

Number of arrangements of n things taken all at a time = P(n, n)

 P(n, r) = \(\frac{n!}{(n-r)!}\)

∴ The total number of ways in which this can be done 

= the number of arrangements of 5 things taken all at a time 

= P(5, 5)

\(\frac{5!}{(5-5)!}\) 

\(\frac{5!}{0!}\) 

{∵ 0! = 1} 

= 5 × 4 × 3 × 2 × 1 

= 120 

Hence,

Number of words, with or without meanings using all the letters of the word ‘DELHI’ are 120.

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