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?