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The numbers of times the digit 3will be written when listing the intiger from 1to 1000

The numbers of times the digit 3will be written when listing the intiger from 1to 1000

Grade:11

1 Answers

Arun
25750 Points
6 years ago
This is P&C question 


Any number between 1 and 999 can be expressed in the form of xyz where 0

Case 1. The numbers in which 3 occurs only once. This means that 3 is one of the digits and the remaining two digits will be any of the other 9 digits 

You have 1*9*9 = 81 such numbers. However, 3 could appear as the first or the second or the third digit. Therefore, there will be 3*81 = 243 numbers (1-digit, 2-digits and 3- digits) in which 3 will appear only once. 

Case 2. The numbers in which 3 will appear twice. In these numbers, one of the digits is not 3 and it can be any of the 9 digits. 
There will be 9 such numbers. However, this digit which is not 3 can appear in the first or second or the third place. So there are 3 * 9 = 27 such numbers. 

In each of these 27 numbers, the digit 3 is written twice. Therefore, 3 is written 54 times.

Case 3. The number in which 3 appears thrice - 333 - 1 number. 3 is written thrice in it. 

Therefore, the total number of times the digit 3 is written between 1 and 999 is 243 + 54 + 3 = 300

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