I)
fist let's find O, that is the number of all numbers between <span>10,000 and 100,000, whose all digits are odd.
so we have to count: 11,111; 11,113; ... 99,999
we notice that all these numbers are 5 digit, and they are made up of the odd digits {1, 3, 5, 7, 9} with repetition allowed.
so there are in total </span>
![5*5*5*5*5= 5^{5}](https://tex.z-dn.net/?f=5%2A5%2A5%2A5%2A5%3D%205%5E%7B5%7D%20)
such numbers.
ii)
E is the total number, of 5-digit numbers formed from the set{0, 2, 4, 6, 8} with repetition allowed, and the first digit not equal to 0.
so
![E=4*5*5*5*5= 4*5^{4}](https://tex.z-dn.net/?f=E%3D4%2A5%2A5%2A5%2A5%3D%204%2A5%5E%7B4%7D)
iii)
![O-E=5^{5}-4*5^{4}=5^{4}(5-4)=5^{4}=625](https://tex.z-dn.net/?f=O-E%3D5%5E%7B5%7D-4%2A5%5E%7B4%7D%3D5%5E%7B4%7D%285-4%29%3D5%5E%7B4%7D%3D625)
Answer: 625