Question

The number of three-digit odd numbers that can be formed with $1,2,3,4,5$ is,

• A. $36$
• B. $60$
• C. $24$
• D. $53$

Answer 1

The correct option is A

$36$

The explanation for the correct option.

The last digit of the number can take one of these $3$ values, $1,3,5$ because number is odd.
The remaining $2$ digits can take any $2$ of the remaining $4$ digits.
$$\begin{gathered} \therefore \mathrm{Total}\mathrm{no}.\mathrm{of}\mathrm{ways}=3\times {}^{4}P_2 \\ \Rightarrow =3\times \frac{4!}{2!} \\ \Rightarrow =3\times \frac{4\times 3\times 2!}{2!} \\ \Rightarrow =36 \end{gathered}$$

Hence, the option $A$is correct.