In a set of numbers from 100 to 1000 inclusive, how many integers are odd and do not contain the digit "5"?
a) 180
b) 196
c) 286
d) 288
e) 324
a) 180
b) 196
c) 286
d) 288
e) 324
Hundereds Digit, Tens Digit, Ones Digit
_ _ _
The numbers that are odd and do not contain the digit 5:
The hundreds digit can be any digit from 1 to 9 but it cannot be 5. So there are a total of 8 possibilities.
The tens digit can be any digit from 0 to 9 but it cannot be 5. So there are a total of 9 possibilities.
The ones digit must be odd so it can be 1, 3, 7, or 9 (it cannot be 5). So there are a total of 4 possibilities.
8 x 9 x 4 = 288
