Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
The word GANESHPURI consists of 4 vowels that have to be arranged in the 5 even places. This can be done in 5! ways.
Now, the remaining 6 consonants can be arranged in the remaining 6 places in 6! ways.
Total number of words in which the vowels occupy even places = 5!\[\times\]6!
APPEARS IN
संबंधित प्रश्न
If (n + 1)! = 90 [(n − 1)!], find n.
Prove that:
Prove that:
If P (5, r) = P (6, r − 1), find r ?
If 5 P(4, n) = 6. P (5, n − 1), find n ?
If P (9, r) = 3024, find r.
If P(11, r) = P (12, r − 1) find r.
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?
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?
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 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?
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?
How many 3-digit even number can be made using the digits 1, 2, 3, 4, 5, 6, 7, if no digits 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 'FAILURE' be arranged so that the consonants may occupy only odd positions?
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 E?
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?
Find the number of words formed by permuting all the letters of the following words:
INDEPENDENCE
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:
PAKISTAN
Find the number of words formed by permuting all the letters of the following words:
EXERCISES
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 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?
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?
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?
If the letters of the word 'LATE' be permuted and the words so formed be arranged as in a dictionary, find the rank of the word LATE.
If the permutations of a, b, c, d, e taken all together be written down in alphabetical order as in dictionary and numbered, find the rank of the permutation debac ?
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.
Evaluate
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 but first letter is a vowel?
How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?
Write the expression nCr +1 + nCr − 1 + 2 × nCr in the simplest form.
