I am trying to solve the following question.
Suppose you select a card at random from a standard deck, and then without putting it back, you select a second card at random from the remaining 51 cards. What is the probability that both cards have the same rank, or both have the same suit, or one is red and one is black (diamonds and hearts-red, clubs and spades-black?
For this problem, can I use the following formula for the union of these three events?
$$P(E\cup F\cup G)=P(E)+P(F)+P(G)-P(E\cap F)-P(E\cap G)-P(F\cap G)+P(E\cap F\cap G)$$
With probability that both cards have same rank being 13/52 * 12/52, probability that both have same suit being 26/52 * 25/52, and probability that one is red and one is black being 1/2 * 1/2? Am I on the right track?