Given that tickets are numbered from 1 to 10.

It is told that two tickets are drawn one after other in random.

We need to find the probability that number on ticket is a multiple of 5 and other number is multiple of 4.

Let us find the individual probabilities first

⇒ P(T₅₁) = P(Number on ticket is multiple of 5 in 1^st draw)

⇒

⇒

⇒

⇒ P(T₄₁) = P(Number on ticket is multiple of 4 in 1^st draw)

⇒

⇒

⇒

⇒ P(T₅₂) = P(Number on ticket is multiple of 5 in 2^nd draw)

⇒

⇒

⇒ P(T₄₂) = P(Number on ticket is multiple of 4 in 2^nd draw)

⇒

⇒

⇒ P(D₅₄) = P(Drawing one ticket which is multiple of 5 and other is multiple of 4)

⇒ P(D₅₄) = P(Drawing 5 multiple ticket first and 4 multiple ticket next) + (P(Drawing 4 multiple ticket first and 5 multiple ticket next)

Since drawing tickets are independent their probabilities multiply each other,

⇒ P(D₅₄) = (P(T₅₁)P(T₄₂)) + (P(T₄₁)P(T₅₂))

⇒

⇒

⇒

∴ The required probability is .