# Combinations and Probability

• Dec 1st 2008, 06:26 PM
algebraisabeast
Combinations and Probability
From a standard deck of 52 cards, 2 cards are drawn with out replacement.
How many combinations of 2 hearts are possible

would I say 13 C 2 to get 78 is this correct?

Also if a family has three kids what is the probability of having one boy?

i know the answer to be 3/8 I did this by writing out each set of possibilities, I was wondering if I am able to do a comb or perm to figure this out.
• Dec 1st 2008, 06:58 PM
Steve_J
Combinations and Probability
1. How many combinations of 2 hearts are possible?
You can draw 1 of 13 the first time, then 1 of the remaining 12 the second time. So I think there would be 13*12 = 156 ways you could daw 2 hearts in two card draws.

2. Also if a family has three kids what is the probability of having one boy?
=Number of ways you can have one boy / number of combinations possible

Number of ways you can have one boy = 3 choose 1 = 3! / (1!*2!) = 3
Number of combinations possible = 2*2*2 = 8 (A boy or girl each time)