The number of arrangements of the word "DELHI" in which E precedes I is
(a) 30
(b) 60
(c) 120
(d) 59
(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 $=24+18+12+6=60$
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