English

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

Advertisements
Advertisements

Question

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

Sum
Advertisements

Solution

There are 8 different letters in the word EQUATION.

Number of words formed from these letters (with or without meaning) = `(8!)/((8 - 8)!) = 8!`

= 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

= 40320

shaalaa.com
  Is there an error in this question or solution?
Chapter 6: Permutations and Combinations - EXERCISE 6.3 [Page 114]

APPEARS IN

NCERT Mathematics [English] Class 11
Chapter 6 Permutations and Combinations
EXERCISE 6.3 | Q 8. | Page 114

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Evaluate 4! – 3!


How many 4-digit numbers are there with no digit repeated?


Find r if `""^5P_r = 2^6 P_(r-1)`


Find x in each of the following:

\[\frac{1}{6!} + \frac{1}{7!} = \frac{x}{8!}\]

A customer forgets a four-digits code for an Automatic Teller Machine (ATM) in a bank. However, he remembers that this code consists of digits 3, 5, 6 and 9. Find the largest possible number of trials necessary to obtain the correct code.


In how many ways can three jobs I, II and III be assigned to three persons A, B and C if one person is assigned only one job and all are capable of doing each job?


How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?


Evaluate each of the following:

6P6 


Write the number of all possible words that can be formed using the letters of the word 'MATHEMATICS'.


Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?


The number of arrangements of the word "DELHI" in which E precedes I is


The number of ways in which the letters of the word 'CONSTANT' can be arranged without changing the relative positions of the vowels and consonants is


The number of ways to arrange the letters of the word CHEESE are


The product of r consecutive positive integers is divisible by


If k + 5Pk + 1 =\[\frac{11 (k - 1)}{2}\]. k + 3Pk , then the values of k are


The number of arrangements of the letters of the word BHARAT taking 3 at a time is


The number of words that can be made by re-arranging the letters of the word APURBA so that vowels and consonants are alternate is


In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?


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


Evaluate the following.

`((3!)! xx 2!)/(5!)`


The possible outcomes when a coin is tossed five times:


The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for all n ∈ N is:


The total number of 9 digit number which has all different digit is:


Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?


A test consists of 10 multiple choice questions. In how many ways can the test be answered if question number n has n + 1 choices?


A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.

How will the answer change if each question may have more than one correct answers?


8 women and 6 men are standing in a line. In how many arrangements will no two men be standing next to one another?


A coin is tossed 8 times, how many different sequences of heads and tails are possible?


A coin is tossed 8 times, how many different sequences containing six heads and two tails are possible?


How many strings are there using the letters of the word INTERMEDIATE, if no two vowels are together


If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then find the ranks of the words
GARDEN


Find the number of strings that can be made using all letters of the word THING. If these words are written as in a dictionary, what will be the 85th string?


Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together


There are 10 persons named P1, P2, P3, ... P10. 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.


In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. How many telephone numbers have all six digits distinct?


Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Determine the number of words which have at least one letter repeated.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×