How many odd integers greater than 500 and less than 1000 have an even digit in the tens place?

Answer 1

Paige:

for the hundreds place you have the possibilities {5,6,7,8,9} 5 choices

for the tens place you have the possibilities {0,2,4,6,8} 5 choices for even digits

for the units place you have the possibilities {1,3,5,7,9} 5 choices.

So, the number of odd integers required will be 5*5*5 (which rule am I using?)

Answer 2

Examine a smaller case:

Of the numbers 1 - 100, 50 are odd, and half of those, 25, have an even 10's digit.

(25)(500) = ?