Question

Two different digits are chosen at random from the set $\{1,2,3,4,5,6,7,8\}.$ Then the probability that both the digits are less than $3,$ is

• A. $\frac{1}{28}$
• B. $\frac{1}{14}$
• C. $\frac{1}{36}$
• D. $\frac{3}{16}$

Answer 1

The correct option is A $\frac{1}{28}$

Total number of ways of selecting $2$ numbers from $8$ is ${}^8{C}_2.$
Only one case is possible when both the digits are less than $3$ i.e., $1$ and $2.$
$\therefore$ Required probability $=\frac{1}{{}^8{C}_2}=\frac{1}{28}$