हिंदी

Find the Number of Words Formed by Permuting All the Letters of the Following Words:Pakistan

Advertisements
Advertisements

प्रश्न

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

PAKISTAN

Advertisements

उत्तर

This word consists of 8 letters that include two As.
The total number of words is the number of arrangements of 7 things, of which 2 are similar to one kind.
⇒\[\frac{8!}{2!}\]= 20160

shaalaa.com
Factorial N (N!) Permutations and Combinations
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 16: Permutations - Exercise 16.5 [पृष्ठ ४२]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 16 Permutations
Exercise 16.5 | Q 1.5 | पृष्ठ ४२

संबंधित प्रश्न

If (n + 1)! = 90 [(n − 1)!], find n.


Prove that: 

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

Prove that:

\[\frac{(2n + 1)!}{n!}\] = 2n [1 · 3 · 5 ... (2n − 1) (2n + 1)]

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


If P (15, r − 1) : P (16, r − 2) = 3 : 4, find r.


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'.


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.


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 'STRANGE' be arranged so that

the vowels occupy only the odd places?


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 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
each word begins with E?


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

all consonants come together?


In how many ways can a lawn tennis mixed double be made up from seven married couples if no husband and wife play in the same set?


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


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


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


How many words can be formed with the letters of the word 'PARALLEL' so that all L's do not come together?


How many number of four digits can be formed with the digits 1, 3, 3, 0?


There are three copies each of 4 different books. In how many ways can they be arranged in a shelf?


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.


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?


Prove that: 4nC2n : 2nCn = [1 · 3 · 5 ... (4n − 1)] : [1 · 3 · 5 ... (2n − 1)]2.


Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
n · n − 1Cr − 1 = (n − r + 1) nCr − 1


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

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

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 (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?


Find the number of permutations of n distinct things taken together, in which 3 particular things must occur together.


Write the number of diagonals of an n-sided polygon.


Write the value of\[\sum^6_{r = 1} \ ^{56 - r}{}{C}_3 + \ ^ {50}{}{C}_4\]


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.


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×