+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?
+118703 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=4∗4!∗5!+5!∗5!9∗9!Prob=5!4!(4+5)9∗9!Prob=5!4!9!Prob=2∗3∗46∗7∗8∗9Prob=16∗7∗3Prob=1126
