Question

How many positive integers less than 1,000 do not have 7 as any digit?

Answer 1

you have 999 integers
between 1 to 100 you got 19 integers
between 100 - 199 again 19
200 - 299 again 19
300 - 399 19
400 - 499 19
500 - 599 19
600 - 699 19
700 - 799 100
800 - 899 19
900 - 999 19

so 999 - (19*9 + 100) = 728

Answer 2

if its including 1000 so 729

Answer 3

729. Use permutation combination

Answer 4

i think with permutations : 9*9*9

Answer 5

Thanx i think i get it now and yea answers 728.

Answer 6

The numbers to be examined are 999 through 1. Restrict the analysis to 3 digit, then 2 digit and finally 1 digit numbers respectively.

The hundreds digit cannot be 7 or 0 which leaves 8 possibilities for that digit. There are 9 digits possible for the tens digits and the ones digit respectively.

The number of numbers two digits long with no 7 in them is 8*9.

The single digit numbers possibilities are 8.

8*9*9 + 8*9 + 8 = 728