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dtan5457
 one year ago
If O represents the number of integers between 10000 and 100000 all whose digits are odd, and E represents all the number of integers between 10000 and 100000 all of whose digits are even, what is the value of OE?
dtan5457
 one year ago
If O represents the number of integers between 10000 and 100000 all whose digits are odd, and E represents all the number of integers between 10000 and 100000 all of whose digits are even, what is the value of OE?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0All numbers within the range have 5 digits. For any one digit, you have 5 choices (1,3,5,7, or 9), so \(O=5^5\). You can determine \(E\) similarly, but keep in mind that the first digit can't be \(0\).

dtan5457
 one year ago
Best ResponseYou've already chosen the best response.0Oh, I get it now. I thought it meant the amount of odd numbers between 10000 and 100000, which would be a lot more

dtan5457
 one year ago
Best ResponseYou've already chosen the best response.0So for E, even numbers, you would have 4 choices (2,4,6,8)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Right, if we're only counting odd numbers we only need to check the last digit. The first digit of every number in \(E\) has 4 choices, yes (2,4,6, or 8), but every digit after that can also be a \(0\), so those have 5 choices.

dtan5457
 one year ago
Best ResponseYou've already chosen the best response.0And since the other digits can be 0, that should be 5^4

dtan5457
 one year ago
Best ResponseYou've already chosen the best response.0so in total O=5^5 E=4x5x5x5x5

dtan5457
 one year ago
Best ResponseYou've already chosen the best response.0and from there it's just basic subtraction

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No problem. You can avoid actually computing the powers, though, and instead make a slight manipulation: \[5^54\times5^4=5^4(54)=5^4\]
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