A five digit number be selected at random. The probability that the digits in the odd place are odd and the even places are even (repetition is not allowed)

Total number of digit used n = 10
Number of odd digits = 5
Number of even digits = 5
Now odd places can be filled by${ }^5{P}_3$ way. Even place
can be filled by ${ }^5{P}_2$ way
i.e., Number of five digit numbers
$\therefore$ Required way for five digit number$= 9 x {10}^4$

$\therefore$ Required probability $=\frac{{ }^5{P}_3{\times }^5{P}_2}{{10}^4\times 9}$