Question

a. What is the probability that a five-card poker hand contains exactly one ace?
b. What is the probability that a five-card poker hand contains cards of five different
kinds?

Answer 1

Part (A):

$\dfrac{\dbinom41\dbinom{48}4}{\dbinom{52}5}\approx0.2995$

Part (B): Depends on what you mean by "different kind". If "kind" means "suit", well that's impossible, because there are only 4 suits so at least two of the cards must match suit.