मराठी

How Many Words Can Be Formed by Arranging the Letters of the Word 'Mumbai' So that All M'S Come Together? - Mathematics

Advertisements
Advertisements

प्रश्न

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

Advertisements

उत्तर

The word MUMBAI consists of 6 letters taht include two Ms.
When we consider both the Ms as a single entity, we are left with 5 entities that can be arranged in 5! ways.
Total number of words that can be formed with all the Ms together = 5! = 120

shaalaa.com
Factorial N (N!) Permutations and Combinations
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 16: Permutations - Exercise 16.5 [पृष्ठ ४३]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 16 Permutations
Exercise 16.5 | Q 6 | पृष्ठ ४३

संबंधित प्रश्‍न

Convert the following products into factorials: 

3 · 6 · 9 · 12 · 15 · 18


If (n + 2)! = 60 [(n − 1)!], find n. 


If (n + 1)! = 90 [(n − 1)!], find n.


Prove that: 

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

If P(11, r) = P (12, r − 1) find r.


If P (n, 4) = 12 . P (n, 2), find n.


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.


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?


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.


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 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 different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:

the letters P and I respectively occupy first and last place?


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?


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

each word begins with O and ends with L?


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:
INDEPENDENCE


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

RUSSIA


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 numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places?


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


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


The letters of the word 'ZENITH' are written in all possible orders. How many words are possible if all these words are written out as in a dictionary? What is the rank of the word 'ZENITH'?


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


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 


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.


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×