हिंदी

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

Advertisements
Advertisements

प्रश्न

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

Advertisements

उत्तर

This word consists of 6 letters that include two Ss and two Es.
The total number of words is the number of arrangements of 6 things, of which 2 are similar to one kind and 2 are similar to the second kind.
⇒\[\frac{6!}{2!2!}\]= 180

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 1.7 | पृष्ठ ४२

संबंधित प्रश्न

Convert the following products into factorials:

1 · 3 · 5 · 7 · 9 ... (2n − 1)


If (n + 1)! = 90 [(n − 1)!], find n.


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

 

 


If P (5, r) = P (6, r − 1), find r ?


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.


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 6 items in column A and 6 items in column B. A student is asked to match each item in column A with an item in column B. How many possible, correct or incorrect, answers are there to this question?


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 'STRANGE' be arranged so that

the vowels come together?

 


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 O and ends with L?


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


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?


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.


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:
ARRANGE


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 with the letters of the word 'UNIVERSITY', the vowels remaining 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?


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


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


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.


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'.


Prove that the product of 2n consecutive negative integers is divisible by (2n)!


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


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  all letters are used at a time 


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


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


Write the maximum number of points of intersection of 8 straight lines in a plane.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×