हिंदी

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 - Mathematics

Advertisements
Advertisements

प्रश्न

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 

उत्तर

There are six letters in the word MONDAY.

 All the letters are used at a time:
This can be done in 6C6 ways.
So, there are 6C6 groups containing six letters that can be arranged in \[6!\]ways.
∴ Number of ways =\[{}^6 C_6 \times 6! = 1 \times 720 = 720\]

shaalaa.com
Factorial N (N!) Permutations and Combinations
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 17: Combinations - Exercise 17.3 [पृष्ठ २३]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 17 Combinations
Exercise 17.3 | Q 3.2 | पृष्ठ २३

संबंधित प्रश्न

Convert the following products into factorials:

5 · 6 · 7 · 8 · 9 · 10


If (n + 2)! = 60 [(n − 1)!], find n. 


Prove that: 

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

If P (n, 5) = 20. P(n, 3), find n ?


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 (n, 5) : P (n, 3) = 2 : 1, find n.


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?


How many three-digit numbers are there, with no digit repeated?


How many 6-digit telephone numbers can be constructed with digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each number starts with 35 and no digit appears more than once?


In how many ways can 6 boys and 5 girls be arranged for a group photograph if the girls are to sit on chairs in a row and the boys are to stand in a row behind them?


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

there is no restriction on letters?


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

each word begins with O and ends with L?


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 but first is vowel.


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:
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 'UNIVERSITY', the vowels remaining 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 different signals can be made from 4 red, 2 white and 3 green flags by arranging all of them vertically on a flagstaff?


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


Find the number of numbers, greater than a million, that can be formed with the digits 2, 3, 0, 3, 4, 2, 3.


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


How many different arrangements can be made by using all the letters in the word 'MATHEMATICS'. How many of them begin with C? How many of them begin with T?


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 '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'.


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


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?


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 


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×