Question

The probability of being dealt all five clubs is the product of the above probabilities. Why is this true and what is this probability?

Answer 1

Assuming the 5 card hand is dealt from a standard randomly shuffled deck of 52 cards, the probability of getting a hand with 5 clubs is


`\frac{\dbinom{13}5\dbinom{39}0}{\dbinom{52}5}=\frac{\dbinom{13}5}{\dbinom{52}5}=(33)/(66640)\approx0.000495`