Advertisements
Advertisements
Question
In how many ways can the letters of the word 'FAILURE' be arranged so that the consonants may occupy only odd positions?
Advertisements
Solution
There are 7 letters in the word FAILURE.
We wish to find the total number of arrangements of these 7 letters so that the consonants occupy only odd positions.
There are 3 consonants and 4 odd positions. These 3 consonants can be arranged in the 4 positions in 4! ways.
Now, the remaining 4 vowels 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
RELATED QUESTIONS
Convert the following products into factorials:
1 · 3 · 5 · 7 · 9 ... (2n − 1)
If (n + 3)! = 56 [(n + 1)!], find n.
Prove that:
If nP4 = 360, find the value of n.
If P (9, r) = 3024, find r.
If P (n − 1, 3) : P (n, 4) = 1 : 9, find n.
If P (n, 5) : P (n, 3) = 2 : 1, 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.
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 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?
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?
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 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 three letter words can be made using the letters of the word 'ORIENTAL'?
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:
SERIES
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 by arranging the letters of the word 'MUMBAI' so that all M's come together?
A biologist studying the genetic code is interested to know the number of possible arrangements of 12 molecules in a chain. The chain contains 4 different molecules represented by the initials A (for Adenine), C (for Cytosine), G (for Guanine) and T (for Thymine) and 3 molecules of each kind. How many different such arrangements are possible?
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 'MOTHER' are written in all possible orders and these words are written out as in a dictionary, find the rank of the word 'MOTHER'.
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?
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
nCr + 2 · nCr − 1 + nCr − 2 = n + 2Cr.
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
Write the number of diagonals of an n-sided polygon.
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.
