1. ## Probability Question

There are 5 four person flats
there are 8 groups of four going for these 5 flats
what is the probability that a particular 3 groups (groups A B and C) all get flats
if its done by random draw.

Thank you

ViperRobK

2. Hello, ViperRobK!

There are 5 four-person flats.
there are 8 groups of four going for these 5 flats.
What is the probability that a particular 3 groups (groups A B and C) all get flats
if its done by random draw?
And why did they make it more confusing than necessary?

There are eight people from which five will be randomly chosen.
What is the probability that 3 particular people (A,B,C) are chosen?

There are: .$\displaystyle _8C_5\:=\:{8\choose5} \:=\:56$ possible outcomes.

There is 1 way for A, B, C to be chosen.
We must choose 2 more people from the other 5 people: .$\displaystyle {5\choose2} \:=\:10$ ways.
. . Hence, there are: .$\displaystyle 1\cdot10\:=\:10$ ways that A,B,C can be chosen.

Therefore: .$\displaystyle P(\text{A,B,C chosen}) \:=\:\frac{10}{56} \:=\:\frac{5}{28}$