Advertisements
Advertisements
प्रश्न
How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?
Advertisements
उत्तर
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
APPEARS IN
संबंधित प्रश्न
Evaluate 8!
How many 4-digit numbers are there with no digit 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?
Find n if n – 1P3 : nP4 = 1 : 9
Find r if `""^5P_r = 2^6 P_(r-1)`
Find r if `""^5P_r = ""^6P_(r-1)`
In how many ways can the letters of the word PERMUTATIONS be arranged if the vowels are all together.
How many numbers of six digits can be formed from the digits 0, 1, 3, 5, 7 and 9 when no digit is repeated? How many of them are divisible by 10 ?
A coin is tossed three times and the outcomes are recorded. How many possible outcomes are there? How many possible outcomes if the coin is tossed four times? Five times? n times?
Find the number of ways in which 8 distinct toys can be distributed among 5 childrens.
In how many ways can 4 prizes be distributed among 5 students, when
(i) no student gets more than one prize?
(ii) a student may get any number of prizes?
(iii) no student gets all the prizes?
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated ?
Evaluate each of the following:
6P6
Write the number of 5 digit numbers that can be formed using digits 0, 1 and 2 ?
Write the number of ways in which 7 men and 7 women can sit on a round table such that no two women sit together ?
Write the number of words that can be formed out of the letters of the word 'COMMITTEE' ?
The number of words that can be formed out of the letters of the word "ARTICLE" so that vowels occupy even places is
The number of words from the letters of the word 'BHARAT' in which B and H will never come together, is
The number of six letter words that can be formed using the letters of the word "ASSIST" in which S's alternate with other letters is
A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is
The product of r consecutive positive integers is divisible by
How many numbers lesser than 1000 can be formed using the digits 5, 6, 7, 8, and 9 if no digit is repeated?
Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.
The number of permutation of n different things taken r at a time, when the repetition is allowed is ______.
Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?
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 each question has four choices?
Find the distinct permutations of the letters of the word MISSISSIPPI?
Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many of these 6-digit numbers are even?
If all permutations of the letters of the word AGAIN are arranged in the order as in a dictionary. What is the 49th word?
Ten different letters of alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated is ______.
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?
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.
In the permutations of n things, r taken together, the number of permutations in which m particular things occur together is `""^(n - m)"P"_(r - m) xx ""^r"P"_m`.
Using the digits 1, 2, 3, 4, 5, 6, 7, a number of 4 different digits is formed. Find
| C1 | C2 |
| (a) How many numbers are formed? | (i) 840 |
| (b) How many number are exactly divisible by 2? | (i) 200 |
| (c) How many numbers are exactly divisible by 25? | (iii) 360 |
| (d) How many of these are exactly divisible by 4? | (iv) 40 |
If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is ______.
If m+nP2 = 90 and m–nP2 = 30, then (m, n) is given by ______.
The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.
