Question

How many positive integers less than 10000 are there which contain at least one 3 or at least one 8 (or both)?

Answer 1

Any positive integer less than 10000 is of the form where all but not all zero .

First we count number of positive integer less than 10000 which does not contains 3 or 8

because all have eight possibilities 0 ,1,2,4,5,6,7,9 . But 00000 is not belongs to this possibility .

Hence number of positive integers less than 10000 which contain at least one 3 or at least one 8 or both is

= 9999 - 4095 , since there are 9999 many positive integers which are less than 10000

= 5904 .

Answer : 5904