Question

A three digit number is to be formed using the digits $3,4,7,8$ and $2$ without repetition. The probability that it is an odd number is

• A. $\frac{2}{5}$
• B. $\frac{1}{5}$
• C. $\frac{4}{5}$
• D. $\frac{3}{5}$

Answer 1

Answer: (A)

$\frac{2}{5}$

Three places of a $3$ digit number can be filled by using $5$ digits in $=5\times 4\times 3=60$ ways.
Number will be odd when either of $3$ or $7$ is at unit's place.
When $3$ is at unit's digit, then remaining $2$ places can be filled by using remaining $4$ digits in $=4\times 3=12$ ways.
Similarly, no. of ways when $7$ is at unit's place $=12$
Favorable no. of ways $=12+12=24$
$\therefore$ Required probability $=\frac{24}{60}=\frac{2}{5}$

Hence, option A.