Final answer:
The probability that a 5-card hand contains cards from at least 3 different suits can be found by calculating the number of favorable outcomes and the total number of possible outcomes.
Step-by-step explanation:
To find the probability that a 5-card hand contains cards from at least 3 different suits, we need to calculate the number of favorable outcomes and the total number of possible outcomes.
The total number of possible 5-card hands from a deck of 52 cards is given by the combination formula: C(52, 5) = 52! / (5! * (52-5)!).
Now, we need to calculate the number of favorable outcomes. There are 4 suits in a deck of cards. We can choose 3 suits in C(4, 3) = 4 ways. For each suit, we can choose 1 card from the suit in C(13, 1) ways. The remaining 2 cards can be chosen from any of the remaining 3 suits in C(39, 2) ways.
Therefore, the probability is P(at least 3 different suits) = (4 * C(13, 1) * C(39, 2)) / C(52, 5).