Final answer:
The probability of getting three aces is 4/22,100. The probability of getting a pair is 13/26. The probability of all three cards having the same suit is 4/22,100.
Step-by-step explanation:
a) To find the probability of getting three aces, we need to calculate the number of ways to choose 3 aces from the 4 aces in the deck, and divide it by the total number of ways to choose 3 cards from the 52 cards in the deck. The number of ways to choose 3 aces from 4 aces is denoted by C(4, 3), which is equal to 4. The total number of ways to choose 3 cards from 52 cards is denoted by C(52, 3), which is equal to 22,100. Therefore, the probability of getting three aces is 4/22,100.
b) To find the probability of getting a pair, we need to calculate the number of ways to choose 2 cards with the same rank from the 13 ranks in the deck, and multiply it by the number of ways to choose 2 suits from the 4 suits in the deck. The number of ways to choose 2 cards with the same rank is denoted by C(13, 2), which is equal to 78. The number of ways to choose 2 suits from the 4 suits is denoted by C(4, 2), which is equal to 6. Therefore, the probability of getting a pair is 78/6, or 13/26.
c) To find the probability that all three cards have the same suit, we need to calculate the number of ways to choose 3 cards with the same suit from the 4 suits in the deck, and divide it by the total number of ways to choose 3 cards from the 52 cards in the deck. The number of ways to choose 3 cards with the same suit is denoted by C(4, 1), which is equal to 4. The total number of ways to choose 3 cards from 52 cards is denoted by C(52, 3), which is equal to 22,100. Therefore, the probability of all three cards having the same suit is 4/22,100.