Advertisements
Advertisements
Question
The number of arrangements of the word "DELHI" in which E precedes I is
Options
30
60
120
59
Advertisements
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
APPEARS IN
RELATED QUESTIONS
Compute `(8!)/(6! xx 2!)`
In how many ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S.
In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?
Find x in each of the following:
Which of the following are true:
(2 × 3)! = 2! × 3!
Find the number of ways in which 8 distinct toys can be distributed among 5 childrens.
In how many ways can 7 letters be posted in 4 letter boxes?
Evaluate each of the following:
Evaluate each of the following:
P(6, 4)
Write the number of 5 digit numbers that can be formed using digits 0, 1 and 2 ?
Write the number of all possible words that can be formed using the letters of the word 'MATHEMATICS'.
Write the number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys ?
Write the number of numbers that can be formed using all for digits 1, 2, 3, 4 ?
The number of permutations of n different things taking r at a time when 3 particular things are to be included is
The number of five-digit telephone numbers having at least one of their digits repeated is
If (n+2)! = 60[(n–1)!], find n
How many 6-digit telephone numbers can be constructed with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each numbers starts with 35 and no digit appear more than once?
Find the rank of the word ‘CHAT’ in the dictionary.
The possible outcomes when a coin is tossed five times:
The total number of 9 digit number which has all different digit is:
If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r
A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if question number n has n + 1 choices?
8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?
Find the distinct permutations of the letters of the word MISSISSIPPI?
In how many ways 4 mathematics books, 3 physics books, 2 chemistry books and 1 biology book can be arranged on a shelf so that all books of the same subjects are together
In how many ways can the letters of the word SUCCESS be arranged so that all Ss are together?
A coin is tossed 8 times, how many different sequences containing six heads and two tails are possible?
Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many of these 6-digit numbers are even?
Find the number of strings that can be made using all letters of the word THING. If these words are written as in a dictionary, what will be the 85th string?
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently is ______.
Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together
The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.
If 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.
8-digit numbers are formed using the digits 1, 1, 2, 2, 2, 3, 4, 4. The number of such numbers in which the odd digits do no occupy odd places is ______.
