मराठी

How Many Permutations Can Be Formed by the Letters of the Word, 'Vowels', Whenthere is No Restriction on Letters?

Advertisements
Advertisements

प्रश्न

How many permutations can be formed by the letters of the word, 'VOWELS', when

there is no restriction on letters?

Advertisements

उत्तर

The word VOWELS consists of 6 distinct letters that can be arranged amongst themselves in 6! ways.
∴ Number of words that can be formed with the letters of the word VOWELS, without any restriction = 6! = 720

shaalaa.com
Factorial N (N!) Permutations and Combinations
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 16: Permutations - Exercise 16.4 [पृष्ठ ३७]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 16 Permutations
Exercise 16.4 | Q 7.1 | पृष्ठ ३७

संबंधित प्रश्‍न

Convert the following products into factorials:

5 · 6 · 7 · 8 · 9 · 10


Convert the following products into factorials: 

3 · 6 · 9 · 12 · 15 · 18


Convert the following products into factorials:

1 · 3 · 5 · 7 · 9 ... (2n − 1)


If (n + 2)! = 60 [(n − 1)!], find n. 


Prove that: 

\[\frac{n!}{(n - r)!}\] = n (n − 1) (n − 2) ... (n − (r − 1))

Prove that:

\[\frac{n!}{(n - r)! r!} + \frac{n!}{(n - r + 1)! (r - 1)!} = \frac{(n + 1)!}{r! (n - r + 1)!}\]


If 5 P(4, n) = 6. P (5, n − 1), find n ?


If P (9, r) = 3024, find r.


If P (2n − 1, n) : P (2n + 1, n − 1) = 22 : 7 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.


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 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?


How many 3-digit even number can be made using the digits 1, 2, 3, 4, 5, 6, 7, if no digits is repeated?


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 never come together? 


How many words can be formed from the letters of the word 'SUNDAY'? How many of these begin with D?


How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:

the vowels are always together?


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.


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:

PAKISTAN


Find the number of words formed by permuting all the letters of the following words:
SERIES


Find the number of words formed by permuting all the letters of the following words:
CONSTANTINOPLE


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 numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places?


How many different numbers, greater than 50000 can be formed with the digits 0, 1, 1, 5, 9.


How many permutations of the letters of the word 'MADHUBANI' do not begin with M but end with I?


Find the number of numbers, greater than a million, that can be formed with the digits 2, 3, 0, 3, 4, 2, 3.


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 the letters of the word
"INTERMEDIATE" be arranged so that:the vowels always occupy even places?


For all positive integers n, show that 2nCn + 2nCn − 1 = `1/2` 2n + 2Cn+1 


Evaluate

\[^ {20}{}{C}_5 + \sum^5_{r = 2} {}^{25 - r} C_4\]

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 


Write the expression nCr +1 + nCr − 1 + 2 × nCr in the simplest form.


Write the total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×