Question

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

Answer 1

Total number of letters = 5
$\therefore$ Total number of words
= Number of arrangements of 5 letters, taken 5 at a time = $5_{P_5}$
= $\frac{5!}{(5-5)!}$
= $\frac{5!}{0!}$
= 5! $[\because 0!=1]$
= $5\times 4\times 3\times 2\times 1$
=120
Hence, the number of words are 120.