Question

The number of arrangements of the word "DELHI" in which E precedes 1 is

• A. 30
• B. 60
• C. 120
• D. 59

Answer 1

The correct option is B

60

There are 4 cases where E precedes 1 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 arrangement

= $4\times 3!=24$

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 letteres inbetween, 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 and have 3 letters in between, which are possible in 1 way whereas other 3 letters are arranged in 3!

So, the number of arrangements

= $1\times 3!=16$

Thus, total number of arrangements

= 24+18+12+6 = 60