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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?

 Apr 24, 2021
 #1
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The answer is 2/25.

 Apr 25, 2021
 #2
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explain??

ss333  Apr 25, 2021
 #3
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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!

 

\(Prob=\frac{4*4!*5!+5!*5!}{9*9!}\\ Prob=\frac{5!4!(4+5)}{9*9!}\\ Prob=\frac{5!4!}{9!}\\ Prob=\frac{2*3*4}{6*7*8*9}\\ Prob=\frac{1}{6*7*3}\\ Prob=\frac{1}{126}\\\)

 Apr 28, 2021

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