(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm having some trouble understanding how to write a sample space in a problem.

Here's an example:

Shuffle a deck of cards and turn over the first card. What is the sample space of this experiment? How many outcomes are in the event that the first card is a heart?

2. Relevant equations

[tex]C_k^n = {n \choose k} = \frac{n!}{k!(n - k)!}[/tex]

3. The attempt at a solution

From what I was explained, sample space is the mutually exclusive and collectively exhaustive set of all possible outcomes. So in my case, wouldn't it be {2-A of hearts, 2-A of spades, 2-A of clubs, 2-A of diamonds} ? Those together create all the possiblities in the deck.

For the second part, isn't it simply 52 choose 13? If it is, it will just be

[tex]{52 \choose 13} = \frac{52!}{13!(52 - 13)!} = 635,013,559,600 \approx 11

6.350135596 \cdot 10^{11}[/tex]

But I'm not sure this is right. There are no answers in my book. If someone could help me on this it would be greatly appreciated.

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# Homework Help: Sample Space

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