When five people are playing a game called hearts, each person is dealt ten cards and the two remain

When five people are playing a game called hearts, each person is dealt ten cards and the two remaining cards are put face down on a table. Because of the rules of the game, it is very important to know the probability of either of the two cards being a heart. What is the probability that at least one card is a heart?

Probability that first card is not a heart is 3/4 since 4 suits in the deck, hearts are 1/4 of the deck.
Since we don't replace cards, the probability of the next card drawn without a heart is (13*3 - 1)/51 = 38/51

Probability of both cards not being hearts is found by multiplying both individual probabilities:
3/4 * 38/51 = 114/204

Having at least one heart is found by subtracting this from 1 which is 204/204:
204/204 - 114/204 = 90/204

This reduces to 15/34