The number of arrangements of the word “DELHI” in which E precedes I is
Question:

The number of arrangements of the word “DELHI” in which E precedes I is

(a) 30

(b) 60

(c) 120

(d) 59

Solution:

(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 $=24+18+12+6=60$