the number of arrangements of the word DELHI in which E precedes I is `30` b. `60` c. `120` d. 59

Explanation

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

`= 4×3! =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 letteres inbetween, which are possible in 2 ways whereas other 3 letters are arranged in `3!`
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