Question

The number of ways in which the five digits 1, 2, 3, 4, 5 can be arranged to make a number greater than 10000 such that the odd digits are in the ascending order,is

• A. 10
• B. 20
• C. 120
• D. 60

Answer 1

The correct option is B 20

The odd digits are $1$,$3$ and $5$
Let's bind these digits with string in the order $1$,$3$,$5$.
now the digits $2$ and $4$ can remain together or separate.
no. of ways they are together =$\left(\begin{array}{c}4\\ 1\end{array}\right)\times 2!=8$
since 4 gaps are created by $1$,$3$,$5$
no. of ways they are separate =$\left(\begin{array}{c}4\\ 2\end{array}\right)\times 2!=12$
Therefore, the total number of such number $=(8+12)=20$