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42 votes
A 5-card hand is dealt from a well-shuffled deck of 52 playing cards. What is the probability that the hand contains cards from at least 3 different suits?

User Acorello
by
3.2k points

2 Answers

17 votes
17 votes

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).

User Moonglum
by
2.5k points
21 votes
21 votes

Answer:

0.2637

Step-by-step explanation:

P(A) = 4 x (13/2) x 13^3/(52/5) = (rounded: 0.264) (Real answer: 0.2637)

User Pewi
by
3.1k points
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