Question

The number of times 3 appear, number writing from 1 to 1000 is:
1. 243
2. 246
3. 297
4. 300

Answer 1

Correct Answer - Option 4 : 300

Given :

The number of times 3 appear 

number writing from 1 to 1000 =?

Calculation :

3 does not occur in 1000 

so we have to count the numbers from 1 to 999 

Number from 1 to 999 is of the form xyz   0 ≤ x , y , z ≤ 9

No. of numbers in which 3 occurs exactly once = ³C₁ × 9 × 9 

No. of numbers in which 3 occurs exactly twice = 3C₂ × 9 

No. of numbers in which 3 occurs exactly thrice = 3C₃

therefore number of times 3 occurs 

⇒  3C1 × 9 × 9 +2 ×  3C2 × 9 + 3 × 3C3

⇒ 243 + 54 + 3 = 300 

∴ the required answer is 300