i)
fist let's find O, that is the number of all numbers between 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 [tex]5*5*5*5*5= 5^{5} [/tex] 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 [tex]E=4*5*5*5*5= 4*5^{4}[/tex]
iii) [tex]O-E=5^{5}-4*5^{4}=5^{4}(5-4)=5^{4}=625[/tex]
Answer: 625
