-aux11.outcomes in card drawing

[karush]

We draw cards from a deck of 52 cards

a) list the sample space if we draw two cards at a time

my ans to this is ((H2,S2)...(C2,D2))

b) How many outcomes do you have in this experiment

but I don't know how they got the answer of 1326

thanks ahead...

 

[Jameson]

Are you familiar with combinations? It's a way of counting groupings when the order doesn't matter. Since for this experiment AhAs is the same as AsAh, then we can say the order doesn't matter and use combinations. So the total number of outcomes is \(\displaystyle \binom{52}{2}\). Do you know how to calculate that?

 

[karush]

my calculator gave

C(52,2) = 1326

so I looked it up $C(n,r) = \frac{n!}{(n-r)!r!}$

However they didn't have this in the text?

 

[Jameson]

Yep, that's the correct formula. I don't know why this isn't in your book. Perhaps they want you to use a more intuitive method. For the first card you have 52 choices and for the second you have 51 choices. However, since order doesn't matter you should divide by 2 since we don't want to count AsAh and AhAs twice. So you have \(\displaystyle \frac{52*51}{2}=1326\). That's exactly the same calculation as \(\displaystyle \binom{52}{2}\) but approaches it from a different way in the set up.

 

[karush]