+0

+1
151
3
+402

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
-1

Apr 25, 2021
#2
+402
0

explain??

ss333  Apr 25, 2021
#3
+114812
+1

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