×

#### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
```
The numbers of time the digit 3 will be written when listing the integers from 1to 1000
The numbers of time the digit 3 will be written when listing the integers from 1to 1000

```
3 years ago

Arun
25768 Points
```							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
```
3 years ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Algebra

View all Questions »

### Course Features

• 731 Video Lectures
• Revision Notes
• Previous Year Papers
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Test paper with Video Solution

### Course Features

• 101 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions