हिंदी

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? - Mathematics

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 are always together?

Advertisements

उत्तर

The word GANESHPURI consists of 4 vowels. If we keep all the vowels together, we have to consider them as a single entity.
So, we are left with the remaining 6 consonants and all the vowels that are taken together as a single entity. This gives us a total of 7 entities that can be arranged in 7! ways.
Also, the 4 vowels can be arranged in 4! ways amongst themselves.

shaalaa.com
Factorial N (N!) Permutations and Combinations
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 16: Permutations - Exercise 16.4 [पृष्ठ ३७]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 16 Permutations
Exercise 16.4 | Q 6.1 | पृष्ठ ३७

संबंधित प्रश्न

Prove that: n! (n + 2) = n! + (n + 1)!


If (n + 2)! = 60 [(n − 1)!], find n. 


If (n + 3)! = 56 [(n + 1)!], find n.


Prove that: 

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

If P (5, r) = P (6, r − 1), find r ?


If P (n, 5) = 20. P(n, 3), find n ?


If P (n − 1, 3) : P (n, 4) = 1 : 9, find n.


Prove that:1 . P (1, 1) + 2 . P (2, 2) + 3 . P (3, 3) + ... + n . P (nn) = P (n + 1, n + 1) − 1.


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 no digit repeated?


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.


In how many ways can the letters of the word 'STRANGE' be arranged so that

the vowels come together?

 


How many words can be formed out of the letters of the word, 'ORIENTAL', so that the vowels always occupy the odd places?


How many words can be formed out of the letters of the word 'ARTICLE', so that vowels occupy even places?


m men and n women are to be seated in a row so that no two women sit together. if m > n then show that the number of ways in which they can be seated as\[\frac{m! (m + 1)!}{(m - n + 1) !}\]


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:
INDEPENDENCE


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


How many words can be formed by arranging the letters of the word 'MUMBAI' so that all M's come together?


How many different signals can be made from 4 red, 2 white and 3 green flags by arranging all of them vertically on a flagstaff?


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 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?


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 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'.


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 ?


Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:

\[\frac{^{n}{}{C}_r}{^{n}{}{C}_{r - 1}} = \frac{n - r + 1}{r}\]

There are 10 persons named\[P_1 , P_2 , P_3 , . . . . , P_{10}\]
Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.


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 number of ways in which 5 red and 4 white balls can be drawn from a bag containing 10 red and 8 white balls.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×