Two dice are thrown independently. Let $$A$$ be the event that the number appeared on the $$1^{st}$$ die is less than the number appeared on the $$2^{nd}$$ die, $$B$$ be the event that the number appeared on the $$1^{st}$$ die is even and that on the second die is odd, and $$C$$ be the event that the number appeared on the $$1^{st}$$ die is odd and that on the $$2^{nd}$$ is even. Then

A

The number of favourable cases of the event $$(A \cup B) \cap C$$ is 6

B

$$A$$ and $$B$$ are mutually exclusive

C

The number of favourable cases of the events $$A$$, $$B$$ and $$C$$ are 15, 6 and 6 respectively

D

$$B$$ and $$C$$ are independent