मराठी

Find the Number of Words Formed by Permuting All the Letters of the Following Words:Exercises - Mathematics

Advertisements
Advertisements

प्रश्न

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

उत्तर

This word consists of 9 letters that include three Es and two Ss.
The total number of words is the number of arrangements of 9 things, of which 2 are similar to one kind and 2 are similar to the second kind.
⇒\[\frac{9!}{2!3!}\]= 30240

shaalaa.com
Factorial N (N!) Permutations and Combinations
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 16: Permutations - Exercise 16.5 [पृष्ठ ४२]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 16 Permutations
Exercise 16.5 | Q 1.8 | पृष्ठ ४२

संबंधित प्रश्‍न

Convert the following products into factorials:

5 · 6 · 7 · 8 · 9 · 10


Convert the following products into factorials: 

(n + 1) (n + 2) (n + 3) ... (2n)


If (n + 3)! = 56 [(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 P (5, r) = P (6, r − 1), find r ?


If P (9, r) = 3024, find r.


If P(11, r) = P (12, r − 1) find r.


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


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 (nn) = P (n + 1, n + 1) − 1.


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


How many words, with or without meaning, can be formed by using all the letters of the word 'DELHI', using each letter exactly 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.


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 '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?

 


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

the vowels occupy only the odd places?


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

all vowels come together?


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

all consonants come together?


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 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:
INTERMEDIATE


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 'PARALLEL' so that all L's do not come together?


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


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


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 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'.


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?


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×