Q. 205.0( 4 Votes )
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
Given, the word ASSASSINATION. It has 13 letters of which repeated letters are A, S, I, and N repeating thrice, 4 times, twice and twice respectively.
We have to find number of words that can formed in such a way that all S’s must come together. For example- ASSSSANNIITO, ININAASSSSATO are few words among them. Notice that all S letters comes in bunch (In bold letters).
A specific method is usually used for solving such type of problems. According to that we assume the group of letters that are remains together (here S, S, S, S) are assumed to be a single letter and all other letters are as usual counted as single letter. Now find number of ways as usual; number of ways of arranging r letters from a group of n letters is equals to nPr. And the final answer is then multiplied by number of ways we can arrange the letters in that group which has to be sticked together in it (Here S, S, S, S).
Since we know, Permutation of n objects taking r at a time is nPr,and permutation of n objects taking all at a time is n!
And, we also know Permutation of n objects taking all at a time having p objects of same type, q objects of another type, r objects of another type is . i.e. the number of repeated objects of same type are in denominator multiplication with factorial.
Letters of word ASSASSINATION: 13
Now from our method, letters are SSSS, A, A, A, I, I, N, N, T, O. (10 letters)
Total number of arrangements of 10 letters
And total number of arrangements of grouped letters (Here S, S, S, S) is , equals 1.
So, our final answer for arranging the letters such that all vowels sticks together equals multiplication of and
Total number of arrangements
Hence, total number of words formed during arrangement of letters of word ASSASSINATION such that all S’s remains together is equals to 151200.
Rate this question :
Which of the following are true :
(2 + 3)! = 2! + 3!RD Sharma - Mathematics
Four letters E, K, S and V, one in each, were purchased from a plastic warehouse. How many ordered pairs of letters, to be used as initials, can be formed from them?RD Sharma - Mathematics
. There are 6 items in column A and 6 items in column B. A student is asked to match each item in column A with an item in column B. How many possible, correct or incorrect, answers are there to this question?RD Sharma - Mathematics
How many permutations can be formed by the letters of the word, ‘VOWELS,’ when
all vowels come together?RD Sharma - Mathematics
Find the total number of ways in which six ‘+’ and four ‘-‘ signs can be arranged in a line such that no two ‘-‘ signs occur together.RD Sharma - Mathematics
In how many ways can the letters of the word “INTERMEDIATE” be arranged so that :
i. the vowels always occupy even places?
ii. the relative order of vowels and consonants do not alter?RD Sharma - Mathematics
From among the 36 teachers in a school, one principal and one vice-principal are to be appointed. In how many ways can this be done?RD Sharma - Mathematics
How many different words can be formed with the letters of word ‘SUNDAY’? How many of the words begin with N? How many begin with N and end in Y?RD Sharma - Mathematics
How many three-digit numbers are there, with distinct digits, with each digit odd?RD Sharma - Mathematics
In how many ways can five children stand in a queue?RD Sharma - Mathematics