Question

A five digit number is chosen at random. The probability that all the digits are distinct and digits at odd places are odd and digits at even places are even is.

• A. $\frac{1}{75}$
• B. $\frac{2}{75}$
• C. $\frac{4}{75}$
• D. None of these
  

Answer 1

The correct option is A $\frac{1}{75}$

The odd places can be filled up in $5\times 4\times 3$ ways and the even places is $5\times 4$ ways.
$\therefore$ the favorable number of ways $5\times 4\times 3\times 5\times 4=5^2.2^4.3$
The number of five digit number $=9\times {10}^4$
Hence the probability the required probability $\frac{5^2.2^4.3}{9\times {10}^4}=\frac{1}{75}$