SATHEE: Permutations And Combinations Question 17

Permutations And Combinations Question 17

Question: How many numbers lying between 10 and 1000 can be formed from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 (repetition is allowed)

Options:

A) 1024

B) 810

C) 2346

D) None of these

Show Answer

Answer:

Correct Answer: B

Solution:

The total number between 10 and 1000 are 989 but we have to form the numbers by using numerals $ 1,\ 2,……..9,\ \ i.e. $ 0 is not occuring so the numbers containing any ?0? would be excluded i.e., Required number of ways $ =989- \begin{cases} & 20,\ 30,\ 40,…………….100=9 \\ & 101,\ 102,……………….200=19 \\ & 201,……………………300=19 \\ & ……………………………………… \\ & ……………………………………… \\ & 901,……………………..990=18 \\ \end{cases} $ $ =989-(9+18+19\times 8)=810 $ . Aliter: Between 10 and 1000, the numbers are of 2 digits and 3 digits. Since repetition is allowed, so each digit can be filled in 9 ways. Therefore number of 2 digit numbers $ =9\times 9=81 $ and number of 3 digit numbers $ 9\times 9\times 9=729 $ Hence total ways $ =81+729=810 $ .

Engineering Preparation

Mathematics 11th

Mathematics 12th

JEE Previous Year Questions

JEE Tutorial Sessions

Medical Preparation

NEET Previous Year Questions

NEET Tutorial Sessions

NCERT Books & Solutions

NCERT Books for JEE

NCERT Books for NEET

NCERT Solutions for JEE

NCERT Solutions for NEET

NCERT Exemplar for JEE

NCERT Exemplar for NEET

Important Resources

Physics Formulas

Chemistry Formulas

Mathematics Formulas

Other Resources

Student Help Booklet

SPOC Help Booklet

Syllabus

Mentorship

Mentorship for JEE

Mentorship for NEET

NCERT Video Solution

NCERT Exemplar Video Solutions

NCERT Exercise Video Solution

BETA

© 2014-2026 Copyright SATHEE

Privacy Policy

Powered by Prutor@IITK

sathee@iitk.ac.in

Media coverage of SATHEE

goolge

Play Store

goolge

App Store

The Ministry of Education has launched the SATHEE initiative in association with IIT Kanpur to provide free guidance for competitive exams. SATHEE offers a range of resources, including reference video lectures, mock tests, and other resources to support your preparation. Please note that participation in the SATHEE program does not guarantee clearing any exam or admission to any institute.

Ask SATHEE

Welcome to SATHEE !
Select from 'Menu' to explore our services, or ask SATHEE to get started. Let's embark on this journey of growth together! 🌐📚🚀🎓

I'm relatively new and can sometimes make mistakes.
If you notice any error, such as an incorrect solution, please use the thumbs down icon to aid my learning.
To begin your journey now, click on I understand

Please select your preferred language
कृपया अपनी पसंदीदा भाषा चुनें