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

#### Ludovico01

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
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 $186368$.

Ludovico01

#### mathman

Forum Staff
If you want probability it is 1/15..