Question

Two-digit numbers are formed using the digits $0,1,2,3,4,5$ where digits are not repeated.
$\text{P}$ is the event that the number so formed is even.
$\text{Q}$ is the event that the number so formed is greater than $50$.
$\text{R}$ is the event that the number so formed is divisible by $3$.
Then write the sample space $\text{S}$ and events $\text{P, Q,}$ and $\text{R}$ using set notation.

Answer 1

$\text{S}=\{10,12,13,14,15,20,21,23,24,25,30,31,32,34,35,40,41,42,43,45,50,51,52,53,54\}$
$\text{P}=\{10,12,14,20,24,30,32,34,40,42,50,52,54\}$
$\text{Q}=\{51,52,53,54\}$
$\text{R}=\{12,15,21,24,30,42,45,51,54\}$