English

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 4 letters are used at a time? - Mathematics

Advertisements
Advertisements

Question

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 4 letters are used at a time?

Answer in Brief

Solution

There are total 6 letters in the word MONDAY.

Total number of words by taking 4 letters out of 6 at a time = `""^("6")"P"_4` = 6 x 5 x 4 x 3 = 360 whereas words can be with or without meaning.

shaalaa.com
Factorial N (N!) Permutations and Combinations
  Is there an error in this question or solution?
Chapter 16: Permutations - Exercise 16.4 [Page 37]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 16 Permutations
Exercise 16.4 | Q 11.1 | Page 37

RELATED QUESTIONS

If P (5, r) = P (6, r − 1), find r ?


If 5 P(4, n) = 6. P (5, n − 1), find n ?


If nP4 = 360, find the value of 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.


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


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?


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?


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?


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

there is no restriction on letters?


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


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:

INDIA


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


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?


Find the total number of permutations of the letters of the word 'INSTITUTE'.


The letters of the word 'SURITI' are written in all possible orders and these words are written out as in a dictionary. Find the rank of the word 'SURITI'.


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 permutations of a, b, c, d, e taken all together be written down in alphabetical order as in dictionary and numbered, find the rank of the permutation debac ?


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


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

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

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

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

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

 nCr + 2 · nCr − 1 + nCr − 2 = n + 2Cr.


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


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


If 35Cn +7 = 35C4n − 2 , then write the values of n.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×