Advertisements
Advertisements
Question
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
Advertisements
Solution
There are total 13 letters in ASSASSINATION, in which A is used three times, S four times, I twice and N twice. 4 – S have to live together. Therefore, it was considered a letter. Thus, 10 letters remain in it in which 3 – A, 2 – 1 and 2 – N are the same.
∴ The arrangement of letters of this word when S remains together
= `(10)/(322)`
= `(10 xx 9 xx 8 xx 7 xx 6 xx 5 xx 4 xx 3 xx 2 xx 1)/((3 xx 2 xx 1)xx(2 xx 1) xx (2 xx 1))`
= 151200
APPEARS IN
RELATED QUESTIONS
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
How many 4-digit numbers are there with no digit repeated?
In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?
In how many ways can three jobs I, II and III be assigned to three persons A, B and C if one person is assigned only one job and all are capable of doing each job?
How many natural numbers less than 1000 can be formed from the digits 0, 1, 2, 3, 4, 5 when a digit may be repeated any number of times?
Find the number of ways in which one can post 5 letters in 7 letter boxes ?
Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?
In how many ways can 7 letters be posted in 4 letter boxes?
Evaluate each of the following:
In how many ways can 4 letters be posted in 5 letter boxes?
In how many ways 4 women draw water from 4 taps, if no tap remains unused?
Write the total number of possible outcomes in a throw of 3 dice in which at least one of the dice shows an even number.
Write the number of words that can be formed out of the letters of the word 'COMMITTEE' ?
Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?
The number of different signals which can be given from 6 flags of different colours taking one or more at a time, is
The number of six letter words that can be formed using the letters of the word "ASSIST" in which S's alternate with other letters is
The number of ways to arrange the letters of the word CHEESE are
Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is
The number of different ways in which 8 persons can stand in a row so that between two particular persons A and B there are always two persons, is
If nP4 = 12(nP2), find n.
In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?
- In how many ways can 8 identical beads be strung on a necklace?
- In how many ways can 8 boys form a ring?
If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r
Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?
Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?
A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.
How will the answer change if each question may have more than one correct answers?
A coin is tossed 8 times, how many different sequences of heads and 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?
If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then find the ranks of the words
GARDEN
Choose the correct alternative:
The product of r consecutive positive integers is divisible b
Suppose m men and n women are to be seated in a row so that no two women sit together. If m > n, show that the number of ways in which they can be seated is `(m!(m + 1)!)/((m - n + 1)1)`
The number of signals that can be sent by 6 flags of different colours taking one or more at a time 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 permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.
If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is ______.
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Determine the number of words which have at least one letter repeated.
