Advertisements
Advertisements
प्रश्न
How many 4-digit numbers are there with no digit repeated?
Advertisements
उत्तर
The thousands place of the 4-digit number is to be filled with any of the digits from 1 to 9 as the digit 0 cannot be included. Therefore, the number of ways in which thousands of places can be filled is 9.
The hundreds, tens, and units place can be filled by any of the digits from 0 to 9. However, the digits cannot be repeated in the 4-digit numbers, and thousands place places are already occupied with a digit. The hundreds, tens, and units place is to be filled by the remaining 9 digits.
Therefore, there will be as many such 3-digit numbers as there are permutations of 9 different digits taken 3 at a time.
Number of such 3-digit numbers
= 9P3 = `(9!)/((9 - 3)!) = (9!)/(6!)`
= `(9 xx 8 xx 7 xx 6!)/(6!) = 9 xx 8 xx 7 = 504`
Thus, by multiplication principle, the required number of 4-digit numbers is 9 × 504 = 4536.
APPEARS IN
संबंधित प्रश्न
Evaluate 8!
if `1/(6!) + 1/(7!) = x/(8!)`, find x
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?
Find r if `""^5P_r = ""^6P_(r-1)`
How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?
In how many ways can the letters of the word PERMUTATIONS be arranged if the vowels are all together.
In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?
Find x in each of the following:
Find x in each of the following:
Which of the following are true:
(2 × 3)! = 2! × 3!
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 natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
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?
Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?
Evaluate each of the following:
8P3
In how many ways 4 women draw water from 4 taps, if no tap remains unused?
Write the number of arrangements of the letters of the word BANANA in which two N's come together.
The number of permutations of n different things taking r at a time when 3 particular things are to be included is
If in a group of n distinct objects, the number of arrangements of 4 objects is 12 times the number of arrangements of 2 objects, then the number of objects is
If k + 5Pk + 1 =\[\frac{11 (k - 1)}{2}\]. k + 3Pk , then the values of k are
The number of ways in which the letters of the word ARTICLE can be arranged so that even places are always occupied by consonants is
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 5 and r = 2.
If (n+2)! = 60[(n–1)!], find n
Evaluate the following.
`(3! + 1!)/(2^2!)`
If n is a positive integer, then the number of terms in the expansion of (x + a)n is:
The number of words with or without meaning that can be formed using letters of the word “EQUATION”, with no repetition of letters is:
Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?
Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?
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.
What is the maximum number of different answers can the students give?
How many strings can be formed from the letters of the word ARTICLE, so that vowels occupy the even places?
If all permutations of the letters of the word AGAIN are arranged in the order as in a dictionary. What is the 49th word?
In how many ways 3 mathematics books, 4 history books, 3 chemistry books and 2 biology books can be arranged on a shelf so that all books of the same subjects are together.
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 ______.
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 three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is ______.
The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.
Number of words from the letters of the words BHARAT in which B and H will never come together is ______.
