- #1
stunner5000pt
- 1,461
- 2
Homework Statement
you and your two friends are with 5 other people who are randomly assigned to two tables of four.
a) calculate the number of possible seating arrangements (where actual placement of your chair does not matter, only relevant placement of individuals at a table)
b) compute the probability of you sit next to your two friends
c) compute the probability that you sit at a different table as your two friends
d) compute the probability that you sit next to your two friends when you know you have been assigned to the same table
2. The attempt at a solution
a) The total number of ways is 8!
b) Confused because if this is a round table (doesnt specify that) has a situation where you don't sit directly next to your friends, as one may be a person away.
Assuming that that is a relevant issue here:
You x 2 possibly ways of friends seated x 5! x 8 (8 different spots for you to sit in)
c) when friends are at a different table: your friends cannot be on your table which is not 1 (you) x 5 x 4 x 3 x (other table) 4 x3x2x1 x 8 (spots for you to sit in)
d) if you know you will sit on the same table, there are two ways that your friends would sit next to you and 4 other ways that they sit on the same table and one of them is NOT next to you so 2/6 or 1/3
Is this correct?
Thank you