# The Number of Arrangements of the Word "Delhi" in Which E Precedes I Is,30,60,120,59 - Mathematics

MCQ

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

• 30

• 60

• 120

• 59

#### Solution

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 x 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 x 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 x 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 x 3!=6
Thus, total number of arrangements=24+18+12+6=60

Concept: Permutations
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 16 Permutations
Q 8 | Page 46