Advertisements
Advertisements
Question
How many permutations can be formed by the letters of the word, 'VOWELS', when
all vowels come together?
Advertisements
Solution
The word VOWELS consists of 2 vowels.
If we keep all the vowels together, we have to consider them as a single entity.
Now, we are left with the 4 consonants and all the vowels that are taken together as a single entity.
This gives us a total of 5 entities that can be arranged in 5! ways.
It is also to be considered that the 2 vowels can be arranged in 2! ways amongst themselves.
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)!
Prove that:
If P (n − 1, 3) : P (n, 4) = 1 : 9, find n.
If P (n, 5) : P (n, 3) = 2 : 1, find n.
If P (15, r − 1) : P (16, r − 2) = 3 : 4, find r.
In how many ways can five children stand in a queue?
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?
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?
Find the number of different 4-letter words, with or without meanings, that can be formed from the letters of the word 'NUMBER'.
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'?
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?
In how many ways can 6 boys and 5 girls be arranged for a group photograph if the girls are to sit on chairs in a row and the boys are to stand in a row behind them?
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?
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 can be formed out of the letters of the word 'ARTICLE', so that vowels occupy even places?
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 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:
INTERMEDIATE
Find the number of words formed by permuting all the letters of the following words:
INDIA
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:
EXERCISES
How many words can be formed with the letters of the word 'PARALLEL' so that all L's do not come together?
How many words can be formed by arranging the letters of the word 'MUMBAI' so that all M's come together?
How many different numbers, greater than 50000 can be formed with the digits 0, 1, 1, 5, 9.
There are three copies each of 4 different books. In how many ways can they be arranged in a shelf?
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'.
The letters of the word 'SURITI' are written in all possible orders and these words are written out as in a dictionary. Find the rank of the word 'SURITI'.
Prove that the product of 2n consecutive negative integers is divisible by (2n)!
For all positive integers n, show that 2nCn + 2nCn − 1 = `1/2` 2n + 2Cn+1
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
nCr + 2 · nCr − 1 + nCr − 2 = n + 2Cr.
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
Write the number of diagonals of an n-sided polygon.
Write the number of ways in which 12 boys may be divided into three groups of 4 boys each.
