मराठी

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

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 

Advertisements

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
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 17: Combinations - Exercise 17.3 [पृष्ठ २३]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 17 Combinations
Exercise 17.3 | Q 3.2 | पृष्ठ २३

संबंधित प्रश्‍न

Convert the following products into factorials:

1 · 3 · 5 · 7 · 9 ... (2n − 1)


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

 

 


If P (9, r) = 3024, find r.


If P (n, 4) = 12 . P (n, 2), find n.


Prove that:1 . P (1, 1) + 2 . P (2, 2) + 3 . P (3, 3) + ... + n . P (n, n) = P (n + 1, n + 1) − 1.


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


If n +5Pn +1 =\[\frac{11 (n - 1)}{2}\]n +3Pn, find n.


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 three-digit numbers are there, with distinct digits, with each digit odd?


How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?


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?


How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?


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 never 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 words can be formed from the letters of the word 'SUNDAY'? How many of these begin with D?


How many permutations can be formed by the letters of the word, 'VOWELS', when
each word begins with E?


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:
EXERCISES


How many words can be formed with the letters of the word 'UNIVERSITY', the vowels remaining together?


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 permutations of the letters of the word 'MADHUBANI' do not begin with M but end with I?


A biologist studying the genetic code is interested to know the number of possible arrangements of 12 molecules in a chain. The chain contains 4 different molecules represented by the initials A (for Adenine), C (for Cytosine), G (for Guanine) and T (for Thymine) and 3 molecules of each kind. How many different such arrangements are possible?


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'.


Find the total number of ways in which six ‘+’ and four ‘−’ signs can be arranged in a line such that no two ‘−’ signs occur together.


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?


Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:

\[\frac{^{n}{}{C}_r}{^{n}{}{C}_{r - 1}} = \frac{n - r + 1}{r}\]

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 but first letter is a vowel?


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 diagonals of an n-sided polygon.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×