English

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

Advertisements
Advertisements

Question

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

PAKISTAN

Advertisements

Solution

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
  Is there an error in this question or solution?
Chapter 16: Permutations - Exercise 16.5 [Page 42]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 16 Permutations
Exercise 16.5 | Q 1.5 | Page 42

RELATED QUESTIONS

Convert the following products into factorials: 

(n + 1) (n + 2) (n + 3) ... (2n)


If (n + 3)! = 56 [(n + 1)!], find n.


If \[\frac{(2n)!}{3! (2n - 3)!}\]  and \[\frac{n!}{2! (n - 2)!}\]  are in the ratio 44 : 3, 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 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.


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?


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 three-digit numbers are there, with no digit 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 come together?

 


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


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 letter G always occupies the first place?


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?


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:
ARRANGE


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?


In how many ways can the letters of the word 'ARRANGE' be arranged so that the two R's are never together?


How many words can be formed from the letters of the word 'SERIES' which start with S and end with S?


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?


Find the total number of permutations of the letters of the word 'INSTITUTE'.


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 ?


In how many ways can the letters of the word
"INTERMEDIATE" be arranged so that:the vowels always occupy even places?


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:

 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 


How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?


Find the number of permutations of n different things taken r at a time such that two specified things occur together?


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 number of ways in which 12 boys may be divided into three groups of 4 boys each.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×