The number of arrangements of the word "DELHI" in which E precede… - Vidyadip

MCQ

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

A
30
✓
60
C
120
D
59

✓

Answer

Correct option: 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 × 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 × 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 × 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 × 3! = 6 Thus, total number of arrangements = 24 + 18 +12 + 6 = 60

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