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

The odd number digits are 1,3,5,7,9.
Total number of odd digits = 5
$\therefore$ Required number of 3 digit numbers
= Number of arrangements of 5 digits by taking 3 at a time = $5_{P_3}$
= $\frac{5!}{(5-3)!}$
= $\frac{5!}{2!}$
= $\frac{5\times 4\times 3\times 2!}{2!}$
= 60
Hence, the total number of 3 digit numbers are 60.