Advertisements
Advertisements
Question
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels occupy only the odd places?
Advertisements
Solution
There are 7 letters in the word STRANGE.
We wish to find the total number of arrangements of these 7 letters so that the vowels occupy only odd positions.
There are 2 vowels and 4 odd positions.
These 2 vowels can be arranged in the 4 positions in 4\[\times\]3 ways, i.e. 12 ways.The remaining 5 consonants can be arranged in the remaining 5 positions in 5! ways.
By fundamental principle of counting:
Total number of arrangements = 12\[\times\]5! = 1440
APPEARS IN
RELATED QUESTIONS
Convert the following products into factorials:
(n + 1) (n + 2) (n + 3) ... (2n)
Prove that: n! (n + 2) = n! + (n + 1)!
If (n + 1)! = 90 [(n − 1)!], find n.
If P (n, 5) = 20. P(n, 3), find n ?
If nP4 = 360, find the value of n.
If P(11, r) = P (12, r − 1) find r.
Prove that:1 . P (1, 1) + 2 . P (2, 2) + 3 . P (3, 3) + ... + n . P (n, n) = P (n + 1, n + 1) − 1.
There are two works each of 3 volumes and two works each of 2 volumes; In how many ways can the 10 books be placed on a shelf so that the volumes of the same work are not separated?
How many three-digit numbers are there, with no digit repeated?
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 never 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 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 permutations can be formed by the letters of the word, 'VOWELS', when
all consonants come together?
How many words can be formed out of the letters of the word 'ARTICLE', so that vowels occupy even places?
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?
Find the number of words formed by permuting all the letters of the following words:
ARRANGE
How many words can be formed with the letters of the word 'UNIVERSITY', the vowels remaining together?
How many words can be formed with the letters of the word 'PARALLEL' so that all L's do not come together?
How many number of four digits can be formed with the digits 1, 3, 3, 0?
How many words can be formed from the letters of the word 'SERIES' which start with S and end with S?
How many different arrangements can be made by using all the letters in the word 'MATHEMATICS'. How many of them begin with C? How many of them begin with T?
How many numbers greater than 1000000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4?
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 permutations of the letters of the word 'INSTITUTE'.
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
n · n − 1Cr − 1 = (n − r + 1) nCr − 1
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
Find the number of permutations of n different things taken r at a time such that two specified things occur together?
If 35Cn +7 = 35C4n − 2 , then write the values of n.
Write the maximum number of points of intersection of 8 straight lines in a plane.
Write the number of ways in which 12 boys may be divided into three groups of 4 boys each.
