# Math Help - 13 card hand

1. ## 13 card hand

Compute the probability that a hand of 13 cards contains:

a) the ace and king of at least one suit.

b) all 4 of at least 1 of the 13 denominations.

2. Originally Posted by cgiulz
Compute the probability that a hand of 13 cards contains:
a) the ace and king of at least one suit.
Suppose that $\mathcal{S}$ is the event that the hand contains the ace and king of spades.
Then $P(\mathcal{S})=\frac{\binom{50}{11}}{\binom{52}{13 }}$.
Now you want to find $P(\mathcal{S}\cup\mathcal{H}\cup \mathcal{C}\cup \mathcal{D})$.