Answer:
84,375
Step-by-step explanation:
Consider the complement of the set of numbers of interest. They will be both even and have one or fewer odd digits.
There are 5^5 = 3,125 numbers with 5 even digits.
There are 4·5^5 = 12,500 numbers with 4 even digits and 1 odd digit in a place other than the least significant digit.
Hence there are 12,500 +3,125 = 15,625 numbers that do not match your requirement. That leaves ...
100,000 - 15,625 = 84,375 numbers of interest
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We have assumed that 00000 through 09999 qualify as 5-digit numbers. If that is not the case, then the total is reduced to 76,875. (3+1)(5^4) = 2500 of the 10,000 numbers in this range do not meet the requirement for being odd or having 2 odd digits. Hence 7500 of the numbers in this range are counted in the above total.
84,375 -7,500 = 76,875 numbers 10000 to 99999 are odd or have at least 2 odd digits.
