How many two-digit numbers have non-zero digits whose sum is odd? For example,54and38.
Two cases.....first digit odd, second even
We have 5 choices for the first digit= 1,3,5,7,9
And we have 4 choices for the second 2,4,6,8
Total = 5 * 4 = 20
Second case......first digit even, second odd
4 choices for the first digit =2,4,6,8
5 choices for the second digit = 1,3,5,7,9
So, again ...20
So
20 + 20 = 40