
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)
A. 1024
B. 810
C. 2346
D. None of these
Answer
509.4k+ views
Hint: In this question you are given a range of numbers 10-1000 and you need to find the total number of numbers which can be formed by using digits 1,2,3,4,5,6,7,8,9. So, divide the solution in two parts, first find the total number of two digit numbers which are greater than 10 then find the total number of three digit numbers. Then add the two to get the required answer to the problem.
Complete step-by-step answer:
Total number of two digit numbers using 1,2,3,4,5,6,7,8,9 = (since repetition is allowed)
So total two-digit numbers = 81
We do not consider the numbers 10,20 ….90 as we are not supposed to use 0 here,hence its 9x9 and not 10x9.
Total number of three-digit numbers using 1,2,3,4,5,6,7,8,9=
So, total three-digit numbers = 729
Total number of numbers lying between 10 and 1000 which can be formed from the digits 1,2,3,4,5,6,7,8,9 = Total two-digit numbers + Total three-digit numbers
= 81+729
=810
So there are 810 numbers between 10-1000 which can be formed by using 1,2,3,4,5,6,7,8,9.
Thus, option B. is correct.
Note: In these types of questions we use the fundamental principle of counting which states that if there are p ways to do one thing, and q ways to do another, then there are p q ways to do both things. This principle can also be used when there are more than two choices involved in the experiment.
Complete step-by-step answer:
Total number of two digit numbers using 1,2,3,4,5,6,7,8,9 =
So total two-digit numbers = 81
We do not consider the numbers 10,20 ….90 as we are not supposed to use 0 here,hence its 9x9 and not 10x9.
Total number of three-digit numbers using 1,2,3,4,5,6,7,8,9=
So, total three-digit numbers = 729
Total number of numbers lying between 10 and 1000 which can be formed from the digits 1,2,3,4,5,6,7,8,9 = Total two-digit numbers + Total three-digit numbers
= 81+729
=810
So there are 810 numbers between 10-1000 which can be formed by using 1,2,3,4,5,6,7,8,9.
Thus, option B. is correct.
Note: In these types of questions we use the fundamental principle of counting which states that if there are p ways to do one thing, and q ways to do another, then there are p
Recently Updated Pages
Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 12 English: Engaging Questions & Answers for Success

Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Social Science: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Chemistry: Engaging Questions & Answers for Success

Trending doubts
Which one is a true fish A Jellyfish B Starfish C Dogfish class 10 biology CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Gautam Buddha was born in the year A581 BC B563 BC class 10 social science CBSE

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE

What is the median of the first 10 natural numbers class 10 maths CBSE
