How many times does the digit 8 appear while writing integers from 1 to 100?

How many times does the digit 8 appear while writing integers from 1 to 100?

**A) 21**

**B) 18**

**C) 20**

**D) 19**

**Ans. C) 20. **

**The digit 8 appear 20 times from 1 to 100.**

This question can be solved easily by using permutation method.

From 1 to 100 there are 1 digit number, 2 digit numbers and three digit numbers also i.e 100 but we can neglect 3 digit numbers because 8 does appear in 100.

When the digit 8 appears on first position

**8 × _**

The 9 digits can be filled in second place i.e 0,1,2,3,4,5,6,7,9

Therefore

**8 9 = 1×9 = 9**

When the digit 8 appears on second position

**_ × 8**

The 9 digits can be filled in first place i.e 0,1,2,3,4,5,6,7,9

__9__ 8 = 9×1 = 9

When the digit 8 is present at first position as well as in second

__8__ × __8__

Fixing both places we get

**1×1 = 1**

But in third case the digit 8 appears two times therefore multiplying it by 2

**1×2 = 2**

Adding 1, 2 and 3 case we get 9+9+2 = 20

**Therefore the digit 8 appear 20 times from 1 to 100 ans.**

**Also read: How many times does the digit 6 appear while writing integers from 400 to 900?**

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