मराठी

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?

Advertisements
Advertisements

प्रश्न

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?

Advertisements

उत्तर

Since the hundred's place cannot be zero, it can be filled by any of the 4 digits (1, 3, 5 and 7).
∴ Number of ways of filling the hundred's place = 4
Since the digits can be repeated in the number, the ten's place and the unit's place can each be filled in 5 ways.
∴ Total numbers = `4xx5xx5=100`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 16: Permutations - Exercise 16.2 [पृष्ठ १६]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 16 Permutations
Exercise 16.2 | Q 38 | पृष्ठ १६

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Evaluate `(n!)/((n-r)!)`, when n = 9, r = 5


How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?


Find r if `""^5P_r = 2^6 P_(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?


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?


Find x in each of the following:

\[\frac{1}{4!} + \frac{1}{5!} = \frac{x}{6!}\]

Which of the following are true:

(2 × 3)! = 2! × 3!


How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?


If three six faced die each marked with numbers 1 to 6 on six faces, are thrown find the total number of possible outcomes ?


Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?


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 ?


Write the number of 5 digit numbers that can be formed using digits 0, 1 and 2 ?


The number of different signals which can be given from 6 flags of different colours taking one or more at a time, 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


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


Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 5 and r = 2.


If nP4 = 12(nP2), find n.


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?


Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.


Evaluate the following.

`(3! xx 0! + 0!)/(2!)`


Evaluate the following.

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


The possible outcomes when a coin is tossed five times:


For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:


The number of words with or without meaning that can be formed using letters of the word “EQUATION”, with no repetition of letters is:


The number of permutation of n different things taken r at a time, when the repetition is allowed is:


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?


8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?


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


How many strings are there using the letters of the word INTERMEDIATE, if the vowels and consonants are alternative


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 divisible by 4?


Choose the correct alternative:
The product of r consecutive positive integers is divisible b


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 ______.


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 ______.


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!

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

Number of words from the letters of the words BHARAT in which B and H will never come together is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×