Home
Class 12
MATHS
The number of times the digit 3 will be ...

The number of times the digit 3 will be written when listing the integers from 1 to 1000, is

A

269

B

271

C

300

D

302

Text Solution

Verified by Experts

The correct Answer is:
C
Since, 3 does not occur inn 1000. so, we have to count the number of times 3 occurs, when we list the integers from 1 to 999.
Any number of between 1 and 999 is of the form xyz, where `0 le x , y, z le9`.
Let us first count the number in which 3 occurs exactly once. since, 3 can occur at one place inn `.^(3)C_(1)` ways, there are `.^(3)C_(1)xx9xx9=243` such numbers. next 3 can occur in exactly two places in `.^(3)C_(2)xx9=27` such numbers. lastly, 3 can occur in all three digits in one number only. hence, the number of times, 3 occcurs is `1xx243+2xx27+3xx1=300`
Promotional Banner

Similar Questions

Explore conceptually related problems

The number of different seven digit numbers that can be written using only three digits 1,2 and 3 with the condition that the digit 2 occurs twice in each number is

The number of numbers that can be formed by using all the digits from 1,2,3,4,3,2,1 so that odd digits occupy odd places, is

The number of 4 digit numbers without repetition that can be formed using the digits 1, 2, 3, 4, 5, 6,7 in which each number has two odd digits and two even digits is

Find a three digit numberwhose consecutive digits form a GP. If we subtract 792 from this number, we get a number consisting of the same digits written in the reverse order. Now, if we increase the second digit of the required number by 2, then the resulting digits will form an AP.

The number of all five digit numbers which are divisible by 4 that can be formed from the digits 0,1,2,3,4 (without repetition) is

The number of 4 digit numbers without repetition that can be formed using the digit 1,2,3,4,5,6,7 in which each number has two odd digits and two digits is

The number of seven digit integers with sum of the digits equal to 10 and formed by using the digits 1,2, and 3 only , is :

Find the number of 4 digit numbers that can be formed using the digits 1,2,3,4,5.If no digits is repeated.

Find the number of 4 - digit numbers that can be formed by using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even ?

Find the number of n digit numbers, which contain the digits 2 and 7, but not the digits 0, 1, 8, 9.