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 = ^{3}C_{1 }× 9 × 9

No. of numbers in which 3 occurs exactly twice = 3C_{2} × 9

No. of numbers in which 3 occurs exactly thrice = 3C_{3}

therefore number of times 3 occurs

⇒ 3C1 × 9 × 9 +2 × 3C2 × 9 + 3 × 3C3

⇒ 243 + 54 + 3 = 300

**∴ the required answer is 300**