Probability using counting techniques
Compute probabilities from a discrete sample space by counting favourable and total outcomes with combinations. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
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A 2-card hand is dealt at random from a standard 52-card deck. What is the probability that the hand is all clubs? Give your answer as a fraction in lowest terms.
Answer: 1/17
See one solved, step by step
A 3-card hand is dealt at random from a standard 52-card deck. What is the probability that the hand is all clubs? Give your answer as a fraction in lowest terms.
📘 Worked solution
1Total number of possible 3-card hands: C(52, 3) = 22100.Count every possible hand, ignoring what's in it.
2Hands that are all clubs: C(13, 3) = 286.There are 13 cards that fit the event; choose 3 of them.
3P = 28622100 = 11850Probability = favourable outcomes / total outcomes, reduced to lowest terms.
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