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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