English

How Many Three-digit Numbers Are There? - Mathematics

Advertisements
Advertisements

Question

How many three-digit numbers are there?

Advertisements

Solution

Available digits for filling any place = {1, 2, 3, 4, 5, 6, 7, 8, 9, 0}
Since the thousand's place cannot be zero, available digits to fill the thousand's place = 9
Number of ways of filling the ten's digit = 10
Similarly, number of ways of filling the unit's digit = 10
∴ Total number of three digit numbers = 9\[\times\]10\[\times\]10 = 900

shaalaa.com
  Is there an error in this question or solution?
Chapter 16: Permutations - Exercise 16.2 [Page 15]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 16 Permutations
Exercise 16.2 | Q 17 | Page 15

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Determine n if  `""^(2n)C_3 : ""^nC_3 = 12 : 1`


In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?


Prove that

\[\frac{1}{9!} + \frac{1}{10!} + \frac{1}{11!} = \frac{122}{11!}\]

There are four parcels and five post-offices. In how many different ways can the parcels be sent by registered post?


There are 5 books on Mathematics and 6 books on Physics in a book shop. In how many ways can a students buy : (i) a Mathematics book and a Physics book (ii) either a Mathematics book or a Physics book?


How many different five-digit number licence plates can be made if

the first-digit cannot be zero, but the repetition of digits is allowed?


In how many ways can six persons be seated in a row?


How many four digit different numbers, greater than 5000 can be formed with the digits 1, 2, 5, 9, 0 when repetition of digits is not allowed?


Evaluate the following:

14C3


Evaluate the following:

12C10


Evaluate the following:

n + 1Cn


If α = mC2, then find the value of αC2.


How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?


There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees:
a particular professor is included.


A sports team of 11 students is to be constituted, choosing at least 5 from class XI and at least 5 from class XII. If there are 20 students in each of these classes, in how many ways can the teams be constituted?


In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.


There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.


In how many ways can a committee of 5 persons be formed out of 6 men and 4 women when at least one woman has to be necessarily selected?


In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?


A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.


A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: at least 3 girls?


How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?


A tea party is arranged for 16 persons along two sides of a long table with 8 chairs on each side. Four persons wish to sit on one particular side and two on the other side. In how many ways can they be seated?


If 20Cr = 20Cr−10, then 18Cr is equal to


If C (n, 12) = C (n, 8), then C (22, n) is equal to


If mC1 nC2 , then


Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?


If C0 + C1 + C2 + ... + Cn = 256, then 2nC2 is equal to


A student has to answer 10 questions, choosing atleast 4 from each of Parts A and B. If there are 6 questions in Part A and 7 in Part B, in how many ways can the student choose 10 questions?


A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Mathematics Part II, unless Mathematics Part I is also borrowed. In how many ways can he choose the three books to be borrowed?


If nCr – 1 = 36, nCr = 84 and nCr + 1 = 126, then find rC2.


In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.


A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if they can be of any colour


In a football championship, 153 matches were played, Every two teams played one match with each other. The number of teams, participating in the championship is ______.


If some or all of n objects are taken at a time, the number of combinations is 2n – 1.


A badminton club has 10 couples as members. They meet to organise a mixed double match. If each wife refers to p artner as well as oppose her husband in the match, then the number of different ways can the match off will be ______.


There are ten boys B1, B2, ...., B10 and five girls G1, G2, ...., G5 in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B1 and B2 together should not be the members of a group is ______.


A regular polygon has 20 sides. The number of triangles that can be drawn by using the vertices but not using the sides is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×