English

How Many Words, with Or Without Meaning, Can Be Formed by Using All the Letters of the Word 'Delhi', Using Each Letter Exactly Once?

Advertisements
Advertisements

Question

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

Advertisements

Solution

There are 5 letters in the word DELHI.
Number of 5 letter words = Number of arrangements of 5 letters, taken 5 at a time
5P5 = 120

shaalaa.com
Factorial N (N!) Permutations and Combinations
  Is there an error in this question or solution?
Chapter 16: Permutations - Exercise 16.3 [Page 28]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 16 Permutations
Exercise 16.3 | Q 21 | Page 28

RELATED QUESTIONS

Convert the following products into factorials:

5 · 6 · 7 · 8 · 9 · 10


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))

Prove that:

\[\frac{(2n + 1)!}{n!}\] = 2n [1 · 3 · 5 ... (2n − 1) (2n + 1)]

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


If P (n, 5) = 20. P(n, 3), find n ?


If P(11, r) = P (12, r − 1) find r.


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


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


Four letters E, K, S and V, one in each, were purchased from a plastic warehouse. How many ordered pairs of letters, to be used as initials, can be formed from them?


Find the number of different 4-letter words, with or without meanings, that can be formed from the letters of the word 'NUMBER'.


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


There are two works each of 3 volumes and two works each of 2 volumes; In how many ways can the 10 books be placed on a shelf so that the volumes of the same work are not separated?


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 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?


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:
INTERMEDIATE


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

INDIA


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


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?


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'?


Evaluate

\[^ {20}{}{C}_5 + \sum^5_{r = 2} {}^{25 - r} C_4\]

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


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

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

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 distinct things taken together, in which 3 particular things must occur together.


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 parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines.


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×