What are the probabilities of sitting next to my best friend?

Jan 2020
2
0
Italy
In my classroom there are 16 people and in each desk there are 2 people.
How many possibilities there are that I sit in the same desk as my best friend?
 

romsek

Math Team
Sep 2015
2,889
1,612
USA
Are desks distinguishable? If not there are $\dbinom{14}{2}=91$ ways you and your friend can sit together at the same desk.

If they are there are $\dbinom{8}{1}\dbinom{14}{2}=728$ ways.

I assume the seats within the desk are indistinguishable. If they are distinguishable add another factor of $2^8$ to get $186368$.
 
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mathman

Forum Staff
May 2007
6,913
762
If you want probability it is 1/15..