So, I have this question i got from a math competition type of book, but it only has the numeric answer only. The question is:
What fraction of all four-digit natural numbers have a product of their digits that is even
The answer supposedly is : 8375/9000 == 67/72
I can understand how to get the denominator of this for the range of all possible 4 digit number from : 1000 -> 9999, the count is 9000.
But in terms of the numerator, I think one needs to go thru cases. Using the property that eveneven = even and oddeven = even. If just one digit is even of the 4 digits then the product of the digits will be even. SO we go thru the cases of one, then 2 then 3 then all 4 even numbers.
Just not sure how to get all the permutations/combinations here. SO need help here.