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.