Probability of Group Repetition in 8 Groups with 16 People

[courtrigrad]

Lets say you have 16 people. You want to make 8 groups. There are 2 people per group. What is the probability that 1 of the 8 groups is the same for a certain number of trials? For example, if person A is with person B this trial, what is the probability that person A will be with person B in the next trial (or many more trials after that)? I know the probability of all the groups being the same is $$\frac{1}{120}$$.

Thanks

 

[courtrigrad]

It was also empirically discovered that the probability of at least one group being the same was 0.4778 . This result was discovered by repeating the experiment 100,000 times.

Anyway thanks a lot

 

[HallsofIvy]

One of the things you will need to do before this can be answered is say HOW you are making the groups. Are you picking people at random (each person equally likely to be chosen)?

 

[courtrigrad]

yes the groups are chosen at random.

 

[courtrigrad]

So if its random, then each group has an equal chance . The probability needs to be a fraction that equals 0.477.

Any help is appreciated

Thanks

 

[courtrigrad]

any ideas?