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if O represents number of integers between 10,000 and 100,000 all of whose digits are odd, and E represents number of integers between 10,000 and 100,000 all of whose digits are even, what is the value of O - E?

Respuesta :

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

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