Advertisements
Advertisements
प्रश्न
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S's are together?
Advertisements
उत्तर
The word ASSASSINATION consists of 13 letters including three As, four Ss, two Ns and two Is.
Considering all the Ss are together or as a single letter, we are left with 10 letters. Out of these, there are three As, two Ns and two Is.
Number of words in which all the Ss are together = Permutations of 10 letters of which three are similar to the first kind, two are similar to the second kind and two are similar to the third kind =\[\frac{10!}{2!2!3!}\]= 151200
APPEARS IN
संबंधित प्रश्न
Convert the following products into factorials:
5 · 6 · 7 · 8 · 9 · 10
Convert the following products into factorials:
1 · 3 · 5 · 7 · 9 ... (2n − 1)
If \[\frac{(2n)!}{3! (2n - 3)!}\] and \[\frac{n!}{2! (n - 2)!}\] are in the ratio 44 : 3, find n.
Prove that:
\[\frac{n!}{(n - r)! r!} + \frac{n!}{(n - r + 1)! (r - 1)!} = \frac{(n + 1)!}{r! (n - r + 1)!}\]
If P (9, r) = 3024, find r.
If P (2n − 1, n) : P (2n + 1, n − 1) = 22 : 7 find n.
If n +5Pn +1 =\[\frac{11 (n - 1)}{2}\]n +3Pn, find n.
In how many ways can five children stand in a queue?
Four books, one each in Chemistry, Physics, Biology and Mathematics, are to be arranged in a shelf. In how many ways can this be done?
How many three-digit numbers are there, with distinct digits, with each digit odd?
If a denotes the number of permutations of (x + 2) things taken all at a time, b the number of permutations of x things taken 11 at a time and c the number of permutations of x − 11 things taken all at a time such that a = 182 bc, find the value of x.
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
All the letters of the word 'EAMCOT' are arranged in different possible ways. Find the number of arrangements in which no two vowels are adjacent to each other.
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels come together?
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?
How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:
the letters P and I respectively occupy first and last place?
How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:
the vowels are always together?
How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:
the vowels always occupy even places?
How many permutations can be formed by the letters of the word, 'VOWELS', when
there is no restriction on letters?
How many permutations can be formed by the letters of the word, 'VOWELS', when
each word begins with O and ends with L?
How many words (with or without dictionary meaning) can be made from the letters in the word MONDAY, assuming that no letter is repeated, if all letters are used at a time.
Find the number of words formed by permuting all the letters of the following words:
INDEPENDENCE
Find the number of words formed by permuting all the letters of the following words:
PAKISTAN
Find the number of words formed by permuting all the letters of the following words:
RUSSIA
In how many ways can the letters of the word 'ALGEBRA' be arranged without changing the relative order of the vowels and consonants?
How many words can be formed with the letters of the word 'PARALLEL' so that all L's do not come together?
How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places?
In how many ways can the letters of the word 'ARRANGE' be arranged so that the two R's are never together?
How many permutations of the letters of the word 'MADHUBANI' do not begin with M but end with I?
How many numbers greater than 1000000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4?
If the letters of the word 'LATE' be permuted and the words so formed be arranged as in a dictionary, find the rank of the word LATE.
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.
The letters of the word 'ZENITH' are written in all possible orders. How many words are possible if all these words are written out as in a dictionary? What is the rank of the word 'ZENITH'?
Prove that: 4nC2n : 2nCn = [1 · 3 · 5 ... (4n − 1)] : [1 · 3 · 5 ... (2n − 1)]2.
Write the value of\[\sum^6_{r = 1} \ ^{56 - r}{}{C}_3 + \ ^ {50}{}{C}_4\]
Write the number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines.
