Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
We note that, there are 3 consonants M, C, T and 3 vowels E, A, O.
Since, no two vowels have to be together, the possible choice for volwels are the blank spaces
These vowels can be arranged in 4P3 ways.
3 consonants can be arranged in 3! ways.
Hence, the required numbers of ways = 3! × 4P3 = 144 ways.
APPEARS IN
संबंधित प्रश्न
Convert the following products into factorials:
5 · 6 · 7 · 8 · 9 · 10
Convert the following products into factorials:
3 · 6 · 9 · 12 · 15 · 18
Convert the following products into factorials:
(n + 1) (n + 2) (n + 3) ... (2n)
If P (n − 1, 3) : P (n, 4) = 1 : 9, find n.
Prove that:1 . P (1, 1) + 2 . P (2, 2) + 3 . P (3, 3) + ... + n . P (n, n) = P (n + 1, n + 1) − 1.
If n +5Pn +1 =\[\frac{11 (n - 1)}{2}\]n +3Pn, find n.
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?
How many three-digit numbers are there, with distinct digits, with each digit odd?
How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?
How many 6-digit telephone numbers can be constructed with digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each number starts with 35 and no digit appears more than once?
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels never come together?
How many words can be formed from the letters of the word 'SUNDAY'? How many of these begin with D?
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 permutations can be formed by the letters of the word, 'VOWELS', when
each word begins with O and ends with L?
m men and n women are to be seated in a row so that no two women sit together. if m > n then show that the number of ways in which they can be seated as\[\frac{m! (m + 1)!}{(m - n + 1) !}\]
Find the number of words formed by permuting all the letters of the following words:
ARRANGE
Find the number of words formed by permuting all the letters of the following words:
CONSTANTINOPLE
How many words can be formed with the letters of the word 'UNIVERSITY', the vowels remaining together?
Find the total number of arrangements of the letters in the expression a3 b2 c4 when written at full length.
In how many ways can the letters of the word 'ARRANGE' be arranged so that the two R's are never together?
How many words can be formed from the letters of the word 'SERIES' which start with S and end with S?
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S's are together?
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.
In how many ways can the letters of the word "INTERMEDIATE" be arranged so that:
the relative order of vowels and consonants do not alter?
For all positive integers n, show that 2nCn + 2nCn − 1 = `1/2` 2n + 2Cn+1
There are 10 persons named\[P_1 , P_2 , P_3 , . . . . , P_{10}\]
Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.
How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if (i) 4 letters are used at a time
How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if all letters are used at a time
How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if all letters are used but first letter is a vowel?
If 35Cn +7 = 35C4n − 2 , then write the values of n.
Write the number of diagonals of an n-sided polygon.
Write the number of ways in which 5 red and 4 white balls can be drawn from a bag containing 10 red and 8 white balls.
