probability of married couples

C

Clifford

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Nov 15, 2006
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there are 8 married couples and two people at random are chosen.

a) what is the probability that these two people are married?
b) what is the probablilty that these two people are of the same sex?
c) if 6 are chosen, what is the proabability that they are 3 married couples?

a) to pick the first person it can by anybody 16/16
their spouse would be 1/15
16/16 * 1/15 = 1/15

b) 16/16 * 7/15 = 7/15

I am not sure if these two are right and I have no idea how to do part c. Could somebody give me a hand?
 
You're correct for a and b.

part c:

There are C(8,3) ways to choose 3 couples from the 8 couples.

Because if we make 8 columns from the 16 people, we have to choose 3 columns from the 8 to have the 3 matching couples.

Let men be A,B,C,D,E,F,G,H and women a,b,c,d,e,f,g,h

We have each with their respective mate:

A,B,C,D,E,F,G,H
a,b,c ,d, e,f, g, h

Also, there are C(16,6) ways to choose 6 people out of 16.

\(\displaystyle \L\\\frac{C(8,3)}{C(16,6)}\)

This seems OK, but I am never totally sure about these infernal counting problems.

I also thought about C(6,3) ways there are 3 married couples out of the 6, but the above seems correct.
 
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