Advertisements
Advertisements
प्रश्न
How many words can be formed out of the letters of the word, 'ORIENTAL', so that the vowels always occupy the odd places?
Advertisements
उत्तर
There are 8 letters in the word ORIENTAL.
We wish to find the total number of arrangements of these 8 letters so that the vowels occupy only odd positions.
There are 4 vowels and 4 odd positions.
These 4 vowels can be arranged in the 4 positions in 4! ways.
Now, the remaining 4 consonants can be arranged in the remaining 4 positions in 4! ways.
By fundamental principle of counting:
Total number of arrangements = 4!\[\times\]4! = 576
APPEARS IN
संबंधित प्रश्न
Prove that: n! (n + 2) = n! + (n + 1)!
If (n + 3)! = 56 [(n + 1)!], find n.
If P (n, 5) = 20. P(n, 3), find n ?
If nP4 = 360, find the value of n.
If P (n, 5) : P (n, 3) = 2 : 1, find n.
In how many ways can five children stand in a queue?
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?
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?
How many words, with or without meaning, can be formed by using all the letters of the word 'DELHI', using each letter exactly once?
How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?
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.
Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, if no digit is repeated? How many of these will be even?
In how many ways can the letters of the word 'FAILURE' be arranged so that the consonants may occupy only odd positions?
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels come together?
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels never come together?
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 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?
In how many ways can a lawn tennis mixed double be made up from seven married couples if no husband and wife play in the same set?
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 4 letters are used at a time?
How many three letter words can be made using the letters of the word 'ORIENTAL'?
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 different numbers, greater than 50000 can be formed with the digits 0, 1, 1, 5, 9.
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 4 red, 3 yellow and 2 green discs be arranged in a row if the discs of the same colour are indistinguishable?
In how many ways can the letters of the word
"INTERMEDIATE" be arranged so that:the vowels always occupy even places?
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?
Prove that: 4nC2n : 2nCn = [1 · 3 · 5 ... (4n − 1)] : [1 · 3 · 5 ... (2n − 1)]2.
Write the number of diagonals of an n-sided polygon.
Write the value of\[\sum^6_{r = 1} \ ^{56 - r}{}{C}_3 + \ ^ {50}{}{C}_4\]
Write the maximum number of points of intersection of 8 straight lines in a plane.
Write the number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines.
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.
Write the number of ways in which 12 boys may be divided into three groups of 4 boys each.
