+407 What fraction of all the 10-digit numbers with distinct digits have the property that the sum of every pair of neighboring digits is odd?
+118687 the total number of numbers is 9*9!
The total number starting with an even and having each consecutive pair adding to an odd is 4*4!*5!
The total number starting with an odd and having each consecutive pair adding to an odd is 5!*5!
\(Prob=\frac{4*4!*5!+5!*5!}{9*9!}\\ Prob=\frac{5!4!(4+5)}{9*9!}\\ Prob=\frac{5!4!}{9!}\\ Prob=\frac{2*3*4}{6*7*8*9}\\ Prob=\frac{1}{6*7*3}\\ Prob=\frac{1}{126}\\\)
