Question

The number of arrangements of the word "DELHI" in which E precedes I is
(a) 30
(b) 60
(c) 120
(d) 59

Answer 1

(b) 60
There are 4 cases where E precedes I i.e.
Case 1: When E and I are together, which are possible in 4 ways whereas other 3 letters are arranged in 3!,
So, the number of arrangements=4$\times$3!=24
Case 2: When E and I have 1 letter in between, which are possible in 3 ways whereas other 3 letters are arranged in 3!,
So,the number of arrangements=3$\times$3!=18
Case 3: When E and I have 2 letters in between, which are possible in 2 ways whereas other 3 letters are arranged in 3!,
So,the number of arrangements=2$\times$3!=12
Case 4: When E and I have 3 letters in between, which are possible in 1 way whereas other 3 letters are arranged in 3!,
So,the number of arrangements=1$\times$3!=6
Thus, total number of arrangements=24+18+12+6=60