Advertisements
Advertisements
प्रश्न
How many numbers of four digits can be formed with the digits 1, 2, 3, 4, 5 if the digits can be repeated in the same number?
उत्तर
The thousand's place can be filled by any of the 5 digits.
∴ Number of ways of filling the thousand's place = 5
Since the digits can repeat in the number, the hundred's place, the ten's place and the unit's place can each be filled in 5 ways.
∴ Total numbers = `5xx5xx5xx5=625`
APPEARS IN
संबंधित प्रश्न
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?
How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
(i) 4 letters are used at a time,
(ii) all letters are used at a time,
(iii) all letters are used but first letter is a vowel?
In how many ways can the letters of the word PERMUTATIONS be arranged if the vowels are all together.
Find x in each of the following:
Find x in each of the following:
Which of the following are true:
(2 +3)! = 2! + 3!
Which of the following are true:
(2 × 3)! = 2! × 3!
Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?
In how many ways can 4 letters be posted in 5 letter boxes?
Write the number of arrangements of the letters of the word BANANA in which two N's come together.
Write the number of words that can be formed out of the letters of the word 'COMMITTEE' ?
Write the number of all possible words that can be formed using the letters of the word 'MATHEMATICS'.
The number of words from the letters of the word 'BHARAT' in which B and H will never come together, 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
If k + 5Pk + 1 =\[\frac{11 (k - 1)}{2}\]. k + 3Pk , then the values of k are
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 5 and r = 2.
Find the rank of the word ‘CHAT’ in the dictionary.
The total number of 9 digit number which has all different digit is:
If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r
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?
Find the distinct permutations of the letters of the word MISSISSIPPI?
How many ways can the product a2 b3 c4 be expressed without exponents?
In how many ways 4 mathematics books, 3 physics books, 2 chemistry books and 1 biology book can be arranged on a shelf so that all books of the same subjects are together
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
Choose the correct alternative:
If `""^(("n" + 5))"P"_(("n" + 1)) = ((11("n" - 1))/2)^(("n" + 3))"P"_"n"`, then the value of n are
The number of signals that can be sent by 6 flags of different colours taking one or more at a time is ______.
The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.
The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is ______.
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.
Five boys and five girls form a line. Find the number of ways of making the seating arrangement under the following condition:
C1 | C2 |
(a) Boys and girls alternate: | (i) 5! × 6! |
(b) No two girls sit together : | (ii) 10! – 5! 6! |
(c) All the girls sit together | (iii) (5!)2 + (5!)2 |
(d) All the girls are never together : | (iv) 2! 5! 5! |
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 |
How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
C1 | C2 |
(a) 4 letters are used at a time | (i) 720 |
(b) All letters are used at a time | (ii) 240 |
(c) All letters are used but the first is a vowel | (iii) 360 |
Let b1, b2, b3, b4 be a 4-element permutation with bi ∈ {1, 2, 3, .......,100} for 1 ≤ i ≤ 4 and bi ≠ bj for i ≠ j, such that either b1, b2, b3 are consecutive integers or b2, b3, b4 are consecutive integers. Then the number of such permutations b1, b2, b3, b4 is equal to ______.
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.