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

$36$

If the number is odd, the last digit can take one of these three values: $1,3,5$

Any two of the remaining four digits can be used for the first two digits.

$\therefore$Total number of ways $=3\times {}^4\mathrm{P}_2$

$=3\times \frac{4!}{\left(4-2\right)!}$ $\left(\because {}^{\mathrm{n}}\mathrm{P}_{\mathrm{r}}=\frac{\mathrm{n}!}{\left(\mathrm{n}-\mathrm{r}\right)!}\right)$

$=3\times \frac{4!}{2!}$

$=3\times \frac{4\times 3\times 2\times 1}{2\times 1}$

$=36$

So, $36$ odd numbers can be formed using these digits.

Therefore, the correct option is A.