Question

Form two digit numbers using $0,1,2,3,4$ without repeating the digits.
P is the event the number formed is even.
Q is the event that the number is divisible by $3$.

Answer 1

$0,1,2,3,4$ if repetition is not allowed at unit place

fill by three numbers $0,2$ or $4$ and tens place occupie other number

$P=3\times 3=9ways$

Q=odd number divisible by $\left(3\right)$ then its sum is multiple of three

$Case-I$ $0,1,2,3$

Number of ways =$3\times 3=9$

$Case-II$ $2,3,4$

number of way=$3\times 2=6$

Total odd numbers are formed $Q=9+6=15$