# Probability a five-card contains the ace of hearts

1. Apr 22, 2008

### zbobet2012

1. The problem statement, all variables and given/known data
What is the probability that a five-card contains the ace of hearts?

2. Relevant equations
$$P(E)=|E|/|S|$$
$$P(E_{1}\bigcup E_{2})=P(E_{1})+P(E_{2}) + P(E_{1}\bigcap E_{2})$$

3. The attempt at a solution
The number of ways to choose 5 cards from 52*the numbers of ways to get an ace from five of those?
$$C(52,5)C(5,1)$$

2. Apr 22, 2008

### exk

mmm, try:

number of ways to choose ace of hearts*number of ways to choose the other 4 cards/number of ways to choose 5 cards from 52.

1*c(51,4)/c(52,5)

that seems better to me.

3. Apr 22, 2008

### zbobet2012

That looks better, thank you very much.