How many numbers are there between 100 to 1000 such that at least one of their digit is 7 ?
between 100 and 1000 means that it is three digit.
CASE1:
when only one digit is 7:
i)when the ones place is 7
it can be done in 8 * 9 * 1 ways
= 72
ii}when the tene place is 7
it can be done in 8*9*1 ways again
= 72 ways
iii) when hundreds place is 7;
it can be done in 9*9 ways
=81 ways
thus when only one digit is 7, it can be done in 72 + 72 +81 ways
=225 ways
CASE2: when two digits are 7
i)when ones and tens place is 7,
it can be done in 8 ways
ii)when hundreds and tens place is 7,
it can be one in 9 ways
iii)when ones and hundreds is 7,
it can be done in 9 ways
total of 26 ways
CASE3; when all three digits are 7
only 1 is possible
thus total no of ways; 225 +26 +1
= 252 ways!